If I'm right, we may have shown the impossibility of a "best' decision theory, no matter how meta you get (in a close analogy to Godelian incompleteness). If I'm wrong, what have I missed?

I would say that any such problem doesn't show that there is no best decision theory, it shows that that class of problem cannot be used in the ranking.

Edited to add: Unless, perhaps, one can show that an instantiation of the problem with particular choice of (in this case decision theory, but whatever is varied) is particularly likely to be encountered.