Are you certain that the likeliness of all your claims being true is not proportional to the size of the change in universe you are claiming to affect.

Almost any person can reasonably claim to be a utility generating god for small values of n for some set of common utility functions (and we don't even have to give up our god-like ability). That is how most of us are able to find gainful employment.

The implausible claim is the ability to generate universe changes of arbitrary utility value.

My proposal is that any claim of utility generation ability has plausibility in inverse proportion to the size of effect that one claims to be able to produce. If I say I can produce delta-U ~$1000, that is somewhat plausible. If I say I can produce delta-U of $1,000,000 that might be plausible for some very high skill people, or given a long time to do it, but as a random person with little time, it's extremely implausible. If I claim to be able to produce delta-U ~ (some amount of wealth > world GDP), that's exceedingly implausible no matter who I am.

And of course, in order to make your mugging function, you would need to be able to produce unbounded utility. Your claim to unbounded utility generation is unboundedly implausible.

Admittedly, this is somewhat unsatisfactory as it effectively treats the unbounded implausibility of a classic onmipotent God figure as an axiom. But this is essentially the same trick as using a Bayesian Occam's Razor to demonstrate atheism. If you aren't happy with this line of reasoning, than I can't see how you'd be happy with Occam's Razor as an axiom, nor how you could legitimately claim that there's a solid rational case for hard atheism.