The problem is that if A is perfectly rational, in a sense, he can't make a credible take it or leave it offer.

I think James meant adding a new limitation to the situation such that there is only one chance to make the deal and one person goes first. ie. Turn it into an ultimatum game.

Do any of the elaborate decision theories popular around these parts solve this problem?

No. At least not if there isn't also a solution specified in Causal Decision Theory. The same problem exists in both. In fact using Timeless Decision Theory makes the problem apply even in the ultimatum game variant. Because even if I was perfectly rational if A offered me $11,000 I would tell him or her to go @#$@#$ @#$@#$.