Regarding Section 3: It appears to me that the plausibility of the Ind principle relies on conflating the mathematical definition of independence with a stronger metaphysical notion. The metaphysical notion is basically exactly what the word "Independent" means intuitively: The results of the coin flips don't depend on each other in any way, whether that's causally or through some other relationship. However, we can easily show that this is not equivalent to the probabilistic notion of independence in scenarios where almost certain events (that is, events whose probability is 1 even though it is possible that they don't happen) exist. Here's a simple example: Let's let X and Y be two independent random variables that are uniformly distributed on [0,1]. We can further say that they don't depend on each other in any way - they are independent in the strong sense. Now define Z as follows: If X is irrational, Z is equal to Y. But if X is rational, Z=0. Is Z independent of X? Well, clearly not by the strong understanding of independence. Z's value explicitly depends on the value of X, and the dependencies don't cancel out. If X is rational, we know for sure that Z=0, so clearly its value is not independent in any strong sense. But, by the definition of "independent" in probability theory, Z is independent of X. Why? Because the probability that X would be rational is 0, although it is still possible (it's almost certain, but not absolutely certain, that X is irrational). And because the probability of X being rational is 0, the dependence of Z on X does not affect the joint probability distribution of Z and X in any way, and thus, they remain probabilistically independent.
To consider a result more similar to the Grim Reaper scenario, we can let x_i represent the results of separate coin flips that have absolutely no effect on each other - they are independent in the strong sense. Clearly, the x_i are mutually independent, both in the sense of probability theory and in the strong metaphysical sense. Now consider y_i defined as follows: If infinitely many of the x_i are heads, then y_i=x_i for every i. Otherwise, y_i=heads for all i. Are the y_i mutually independent? In the sense of probability theory, yes. But clearly, the values of the y_i do depend on each other: One of the y_i can only be tails if infinitely many of the other y_i are heads. It's just that this dependency only affects the values of the y_i with probability 0, and thus it can't be picked up on by the probabilistic notion of independence.
The core of the issue here is that, because probability is a real-valued measure on a probability space that may contain uncountably many points, it lacks the ability to pick up on very fine distinctions that the measure is too coarse-grained to detect. In particular, probability cannot distinguish an event that is impossible (i.e., the set of points in the probability space corresponding to that event is empty) from one that is almost certain not to happen (i.e., one that consists of a nonempty set with zero measure). You also can't condition on zero-probability events in standard probability theory, which prevents you from noticing the dependencies that would be obvious if you could (Intuitively, we could create a conditional probability distribution for Z considitioned on X being rational, that would just give a 100% probability to Z=1. This is not equal to the unconditional probability distribution, thus showing Z to depend on X. Likewise, if we could condition on the values of cofinite subsets of {y_i}, we would intuitively expect to find probabilities for the remaining values that differ from the unconditional probabilities. But in standard probability theory, all these conditionals are undefined.)
So how does this all connect back to Koons's argument? Well, I think the Ind principle is pretty plausible if "independent" is understood in the metaphysical sense. But it poses no problem for RPInf or the UPD. After all, it's logically impossible to have a series of coin flips that don't depend on each other in any way, but that also depend on each other in such a way that it's impossible for them all to land tails. Thus, the Chancy Grim Reaper story is logically impossible under the strong understanding of independence, regardless of how the coin flips turn out, so proponents of RPInf need not endorse the possibility of Lucky. We can accept both Ind and RPInf without contradiction.
On the other hand, if we understand independence in the purely probabilistic sense, under standard probability theory, there's just no reason whatsoever to believe Ind. The entire motivation for Ind is that if a set of chancy events each have a set of possible outcomes, and the outcomes of the events don't affect each other, then any combination of outcomes should be possible because, if some combination of outcomes was impossible, that would be a dependence between those outcomes. But we've just shown that independence in the probabilistic sense doesn't mean that the outcomes of events don't affect each other, and that you can have a combination of possible outcomes of events be impossible even while those events remain probabilistically independent. The entire reason we needed to specify independence in Ind is that it's obviously possible to create an impossible scenario by changing the outcomes of chancy events that depend on each other in order to make them incompatible. But it turns out that probabilistically independent events can still depend on each other in such a way that certain combinations are incompatible, as long as those combinations would have probability zero even if the events truly had no dependence between them. Once this is realized, Ind becomes not just unmotivated, but obviously false, in the same way that a principle similar to Ind but which didn't specify independence would be obviously false. Of course, one might try to fix Ind by specifying that it only applies to combinations of events that have nonzero probability or something like that, but once you do that, Koons's argument no longer works because Unlucky scenarios have probability zero. It's impossible for him to create a version of the unlucky scenario that doesn't have probability zero because he's been unknowingly exploiting the fact that zero-probability events in a sense don't get "counted" when determining independence in order to construct his example.
tldr: I agree with everything you say in Section 3.2, and I go further by showing that the probabilistic notion of "independence" doesn't fit the intuitive definition of the term, and that Ind is almost certainly false if it uses this definition. If we define independence more in line with the intuitive meaning, then either Case 1 or Case 2 of your trilemma holds, depending on whether we stipulate this notion of independence as part of the Chancy Reaper story. Any attempt to modify Ind to get to Case 3 will fail because the argument relies on ignoring zero-probability possible events in the definition of "independent" and then explicitly considering zero-probability events in the Chancy Reaper story.
BTW great article so far (I've only reads Sections 1-3 as of writing this but wanted to get my thoughts down in case I forget later).
Regarding Section 3: It appears to me that the plausibility of the Ind principle relies on conflating the mathematical definition of independence with a stronger metaphysical notion. The metaphysical notion is basically exactly what the word "Independent" means intuitively: The results of the coin flips don't depend on each other in any way, whether that's causally or through some other relationship. However, we can easily show that this is not equivalent to the probabilistic notion of independence in scenarios where almost certain events (that is, events whose probability is 1 even though it is possible that they don't happen) exist. Here's a simple example: Let's let X and Y be two independent random variables that are uniformly distributed on [0,1]. We can further say that they don't depend on each other in any way - they are independent in the strong sense. Now define Z as follows: If X is irrational, Z is equal to Y. But if X is rational, Z=0. Is Z independent of X? Well, clearly not by the strong understanding of independence. Z's value explicitly depends on the value of X, and the dependencies don't cancel out. If X is rational, we know for sure that Z=0, so clearly its value is not independent in any strong sense. But, by the definition of "independent" in probability theory, Z is independent of X. Why? Because the probability that X would be rational is 0, although it is still possible (it's almost certain, but not absolutely certain, that X is irrational). And because the probability of X being rational is 0, the dependence of Z on X does not affect the joint probability distribution of Z and X in any way, and thus, they remain probabilistically independent.
To consider a result more similar to the Grim Reaper scenario, we can let x_i represent the results of separate coin flips that have absolutely no effect on each other - they are independent in the strong sense. Clearly, the x_i are mutually independent, both in the sense of probability theory and in the strong metaphysical sense. Now consider y_i defined as follows: If infinitely many of the x_i are heads, then y_i=x_i for every i. Otherwise, y_i=heads for all i. Are the y_i mutually independent? In the sense of probability theory, yes. But clearly, the values of the y_i do depend on each other: One of the y_i can only be tails if infinitely many of the other y_i are heads. It's just that this dependency only affects the values of the y_i with probability 0, and thus it can't be picked up on by the probabilistic notion of independence.
The core of the issue here is that, because probability is a real-valued measure on a probability space that may contain uncountably many points, it lacks the ability to pick up on very fine distinctions that the measure is too coarse-grained to detect. In particular, probability cannot distinguish an event that is impossible (i.e., the set of points in the probability space corresponding to that event is empty) from one that is almost certain not to happen (i.e., one that consists of a nonempty set with zero measure). You also can't condition on zero-probability events in standard probability theory, which prevents you from noticing the dependencies that would be obvious if you could (Intuitively, we could create a conditional probability distribution for Z considitioned on X being rational, that would just give a 100% probability to Z=1. This is not equal to the unconditional probability distribution, thus showing Z to depend on X. Likewise, if we could condition on the values of cofinite subsets of {y_i}, we would intuitively expect to find probabilities for the remaining values that differ from the unconditional probabilities. But in standard probability theory, all these conditionals are undefined.)
So how does this all connect back to Koons's argument? Well, I think the Ind principle is pretty plausible if "independent" is understood in the metaphysical sense. But it poses no problem for RPInf or the UPD. After all, it's logically impossible to have a series of coin flips that don't depend on each other in any way, but that also depend on each other in such a way that it's impossible for them all to land tails. Thus, the Chancy Grim Reaper story is logically impossible under the strong understanding of independence, regardless of how the coin flips turn out, so proponents of RPInf need not endorse the possibility of Lucky. We can accept both Ind and RPInf without contradiction.
On the other hand, if we understand independence in the purely probabilistic sense, under standard probability theory, there's just no reason whatsoever to believe Ind. The entire motivation for Ind is that if a set of chancy events each have a set of possible outcomes, and the outcomes of the events don't affect each other, then any combination of outcomes should be possible because, if some combination of outcomes was impossible, that would be a dependence between those outcomes. But we've just shown that independence in the probabilistic sense doesn't mean that the outcomes of events don't affect each other, and that you can have a combination of possible outcomes of events be impossible even while those events remain probabilistically independent. The entire reason we needed to specify independence in Ind is that it's obviously possible to create an impossible scenario by changing the outcomes of chancy events that depend on each other in order to make them incompatible. But it turns out that probabilistically independent events can still depend on each other in such a way that certain combinations are incompatible, as long as those combinations would have probability zero even if the events truly had no dependence between them. Once this is realized, Ind becomes not just unmotivated, but obviously false, in the same way that a principle similar to Ind but which didn't specify independence would be obviously false. Of course, one might try to fix Ind by specifying that it only applies to combinations of events that have nonzero probability or something like that, but once you do that, Koons's argument no longer works because Unlucky scenarios have probability zero. It's impossible for him to create a version of the unlucky scenario that doesn't have probability zero because he's been unknowingly exploiting the fact that zero-probability events in a sense don't get "counted" when determining independence in order to construct his example.
tldr: I agree with everything you say in Section 3.2, and I go further by showing that the probabilistic notion of "independence" doesn't fit the intuitive definition of the term, and that Ind is almost certainly false if it uses this definition. If we define independence more in line with the intuitive meaning, then either Case 1 or Case 2 of your trilemma holds, depending on whether we stipulate this notion of independence as part of the Chancy Reaper story. Any attempt to modify Ind to get to Case 3 will fail because the argument relies on ignoring zero-probability possible events in the definition of "independent" and then explicitly considering zero-probability events in the Chancy Reaper story.
BTW great article so far (I've only reads Sections 1-3 as of writing this but wanted to get my thoughts down in case I forget later).