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.