Hey Jeffhe- the position you put forward looks structurally really similar to elements of Scanlon’s, and you discuss a dillema that is often discussed in the context of his work (the lifeboat/the rocks example)- It also seems like given your reply to objection 3 you might really like it’s approach (if you are not familiar with it already). Subsection 7 of this SEP article (https://plato.stanford.edu/entries/contractualism/) gives a good overview of the case that is tied to the one you discuss. The idea of the separateness of persons, and the idea that one persons pain can’t cancel out another person pain, is well represented in Scanlon’s work.
I also wonder whether the right way of representing an ‘equal chance of being helped’ in this model is not to flip a coin for each group, but to roll a N sided dice, where N are the total number of people who could be helped, and then choosing whichever group the person whose number is rolled is in: that way everyone, in some sense, has a chance to be saved, and that chance is, in some sense, equal- without leading to the worrying conclusions that Bob and a million peoples lives ought to be settled through a coin flip (The coin-flipping decision theory could also be abused by dividing up groups differently, i.e. I can always re-describe the world in the way where a person I could help in extreme pain is in one group, and all other people are in a different group, but then I can simply redescribed the world to move that person into the ‘all other people’ category, and select another person, which seems to mean we can arbitrarily increase the odds of any one person being the right person to help, simply by moving them between the categories- which seems wrong).
Just wanted to chime in and say I think this is a really great idea! Looking forward to seeing the program grow in the years to come!