Changes to BIP-360 - Pay to Quantum Resistant Hash (P2QRH)

This is a cool idea, though I rather make as few changes in P2QRH as possible.

If I understand you correctly this would prevent long exposure attacks on reused public keys, but not solve short exposure attacks.

You don’t need to change P2QRH to get this. Simply require a preimage and a signature (H(x) == y AND VER(pk, sig, m) == 1) to spend and have a different preimage per leaf. This prevents long exposure attacks even if the public key is reused since the attacker doesn’t know the preimage x. This seems like not reusing a public key but with extra steps.

In P2SH you can do slightly better using the techniques from Signing a Bitcoin Transaction with Lamport Signatures (no changes needed). Though as pointed out by Adam Borcany this scheme functions more like a speed bump since due to the 201 opcode limit in pre-tapscript the key space is small enough to be vulnerable to bruteforce.

You should write this up more concretely. It is an interesting idea.