But we don't yet to have a clear, mathematically precise way to explain why we should also respond negatively to "give me a dollar, and I'll use my Matrix Lord powers to save 3^^^3 lives."

Yes, we do: bounded utility functions work just fine without any mathematical difficulties, and seem to map well to the psychological mechanisms that produce our intuitions. Objections to them are more philosophical and person-dependent.

The problem with Pascal's mugging doesn't lie merely in the particular hoped-for payoff, it's that in extreme combinations of small chance/large payoff, the complexity of certain hypotheses doesn't seem sufficient to adequately (as per our intuitions) penalize said hypotheses.

If we are going to be invoking intuition, then we should be careful about using examples with many extraneous intuition-provoking factors, and in thinking about how the intuitions are formed.

For example, handing over $1 to a literal Pascal's Mugger, a guy who asks for the money out of your wallet in exchange for magic outputs, after trying and failing to mug you with a gun (which he found he forgot at home), is clearly less likely to get a big finite payoff than other uses of the money. The guy is claiming two things: 1) large payoffs (in things like life-years or dollars, not utility, which depends on your psychology) are physically possible 2) conditional on 1, the payoffs are more likely from paying him than other uses of money. Realistic amounts of evidence won't be enough to neutralize 1), but would easily neutralize 2).

Heuristics which tell you not to pay off the mugger are right, even for total utilitarians.

Moreover, many of our intuitions look to be heuristics trained with past predictive success and delivery of individual rewards in one's lifetime. If you save 1000 lives, trillions of person-seconds, you will not get billions of times the reinforcement you would get from eating a chocolate bar. You may get a 'warm glow' and some social prestige for success, but this will be a reward of ordinary scale in your reinforcement system, not enough to overcome astronomically low probabilities. So learned intuitions will tend to move you away from what would be good deals for an aggregative utilitarian, since they are bad deals in terms of discounted status and sex and chocolate.

Peter Singer argues that we should then discount those intuitions trained for non-moral purposes. Robin Hanson might argue that morality is overrated relative to our nonmoral desires. But it is worth attending to the processes that train intuitions, and figuring out which criteria one endorses.