This doesn't work with an unbounded utility function, for standard reasons:

1) The mixed strategy. If there is at least one lottery with infinite expected utility, then any combination of taking that lottery and other actions also has infinite expected utility. For example, in the traditional Pascal's Wager involving taking steps to believe in God, you could instead go around committing Christian sins: since there would be nonzero probability that this would lead to your 'wagering for God' anyway, it would also have infinite expected utility. See Alan Hajek's classic article "Waging War on Pascal's Wager."

Given the mixed strategy, taking and not taking your bet both have infinite expected utility, even if there are no other infinite expected utility lotteries.

2) To get a decision theory that actually would take infinite expected utility lotteries with high probability we would need to use something like the hyperreals, which would allow for differences in the expected utility of different probabilities of infinite payoff. But once we do that, the fact that your offer is so implausible penalizes it. We can instead keep our money and look for better opportunities, e.g. by acquiring info, developing our technology, etc. Conditional on there being any sources of infinite utility, it is far more likely that they will be better obtained by other routes than by succumbing to this trick. If nothing else, I could hold the money in case I encounter a more plausible Mugger (and your version is not the most plausible I have seen). Now if you demonstrated the ability to write your name on the Moon in asteroid craters, turn the Sun into cheese, etc, etc, taking your bet might win for an agent with an unbounded utility function.

Also see Nick Bostrom's infinitarian ethics paper.

As it happens I agree that human behavior and intuitions (as I weight them) in these situations are usually better summed up with a bounded utility function, which may include terms like the probability of attaining infinite welfare, or attaining a large portion of hyperreal expected welfare that one could, etc, than an unbounded utility function. I also agree that St Petersburg lotteries and the like do indicate our bounded preferences. The problem here is technical, in the construction of your example.