The obvious solution is that I, as an incredibly powerful omnipotent god being, will mug anyone who spends too many resources dealing with pascals mugging style issues. If you have sufficient evidence that your particular example outweighs the risk of me doing that, then it's not exactly a pascals mugging, is it?
At the very least it shows there's a point behind which it's no longer useful to consider a very small probability in your utility calculation. That point is where the probability of your hypothesis being true is close to being as probable as my claim being true. So now the big question is "how unlikely is my claim"?
What do we do when there is a very tiny (2^-x) chance that THIS random thing has incredibly huge (O(3^^^^3)) importance?
Now I tend not to follow this form very much, so please excuse me if this has been suggested before. Still, I don't know that there's anyone else on this board who could actually carry out these threats.
If anyone accepts a pascals mugging style trade off with full knowledge of the problem, then I will slowly torture to death 3^^^^3 sentient minds. Or a suitably higher number if they include a higher (plausible, from my external viewpoint) number. Rest assured I can at least match their raw computing power from where I am. Good luck.
EDIT: I'm told that Eleizer proposed a similar solution over here, although more eloquently then I have.