Well, here's the paradox: strict one-boxers in transparent Newcomb argue that they must one-box always, even when the box is empty, and therefore the boxes will be full.

No, they argue that they must one-box always, even when they think they see the box is empty.

The argument is that you can't do the Bayesian update P(the box is empty | I see the box as empty) = 1, because Bayesian updating in general fails to "win" when there are other copies of you in the same world, or when others can do source-level predictions of you. Instead, you should use Updateless Decision Theory.

BTW, I don't think UDT is applicable to most human decisions (or rather, it probably tells you to do the same things as standard decision theory), including things like voting or contributing to charity, or deciding whether to have children, because I think logical correlations between ordinary humans are probably pretty low. (That's just an intuition though since I don't know how to do the calculations.)