I now think that Newcomb's problem is simply an exceptional situation where there is an artificial incentive to employ something other than CDT, and that most such situations can be dealt with by being a CDT agent who can self-modify.

Eric Barnes had got this far in 1997 - saying:

I conclude that the rational action for a player in the Newcomb Paradox is taking both boxes, but that rational agents will usually take only one box because they have rationally adopted the disposition to do so.