Another way to phrase it is that this problem is isomorphic to the transparent box Newcomb problem, and you are trying to find a formalized decision theory that will one-box the empty box "knowing" it is empty. (Just that instead of "knowing" through updating on seeing the empty box, which UDT refuses to do, there is an equivalent trick with the dependence.) The only way you can do that is if you either don't actually try to maximize the money at that point or expect a contradiction. Not trying to maximize the money in such situations probably is easier to deal with.