I think I have a better understanding now.

For every statement S and for every action A, except the A Myself() actually returns, PA will contain a theorem of the form (Myself()=A) => S because falsehood implies anything. Unless Myself() doesn't halt, in which case the value of Myself() can be undecidable in PA and Myself's theorem prover wont find anything, consistent with the fact that Myself() doesn't halt.

I will assume Myself() is also filtering theorems by making sure Universe() has some minimum utility in the consequent.

If Myself() halts, then if the first theorem it finds has a false consequent PA would be inconsistent (because Myself() will return A, proving the antecedent true, proving the consequent true). I guess if this would have happened, then Myself() will be undecidable in PA.

If Myself() halts and the first theorem it finds has a true consequent then all is good with the world and we successfully made a good decision.

Whether or not ambient decision theory works on a particular problem seems to depend on the ordering of theorems it looks at. I don't see any reason to expect this ordering to be favorable.