Yes, I hadn't much considered replay withholding which would indeed be a bit of a big problem.  Even without a cost to play, replays could be withheld waiting for some high-tx-fee block, or a large collection of replays could be built up to force forks and double-spend.

However, I think I've realized that there are some even bigger problems with my proposal, and I think it would not effectively serve to secure transactions as described without additional side-band hashing strength, like HUC has.

I'll keep thinking on it, but I think eliminating the map reset would not be as easy/straightforward as I first thought.