Additional privacy is basically a non-factor in this attack but, as an academic point, if anything it actually hurts rather than helps. On Bitcoin you could send spoof transactions (from yourself to yourself) to 'fill' your empty blocks if that were needed for some reason, and you can do the same on e.g. MimbleWimble except no-one can tell blocks or addresses apart at all.

Switching to PoS is indeed an option, though the word 'hope' is doing a lot of work in your answer! I haven't looked at it in the same depth but I know most Bitcoiners have torn it to shreds as an option.