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?

You're right. However, since all decision theories fail when confronted with their personal version of this problem, but may or may not fail in other problems, then some decision theories may be better than others. The one that is better than all the others is thus the "best" DT.