One the one hand, this is a good point that points out a weakness in my argument - if states are continuous rather than discrete, one can increase or decrease entropy even with deterministic time-evolution by spreading out or squeezing probability mass.

But I don't know how far outside the microcanonical this analogy you're making holds. Exchanging energy definitely works like exchanging particles when all you know is the total energy, but there's no entropy increase when both are in a single microstate, or when both have the same Boltzmann distribution (hm, or is there?).

I'll think about it too.