1) We don’t need an unbounded utility function to demonstrate Pascal’s Mugging. Plain old large numbers like 10^100 are enough.
2) It seems reasonable for utility to be linear in things we care about, e.g. human lives. This could run into a problem with non-uniqueness, i.e., if I run an identical computer program of you twice, maybe that shouldn’t count as two. But I think this is sufficiently murky as to not make bounded utility clearly correct.
Rolling all 60 years of bets up into one probability distribution as in your example, we get:
0,999999999998 chance of − 1 billion * cost-per-bet
1 − 0,999999999998 - epsilon chance of 10^100 lives − 1 billion * cost-per-bet
epsilon chance of n * 10^100 lives, etc.
I think what this shows is that the aggregating technique you propose is no different than just dealing with a 1-shot bet. So if you can’t solve the one-shot Pascal’s mugging, aggregating it won’t help in general.