Thanks for the idea, Anthony!
I assume the Schnorr challenge would be changed to commit to H(Q) instead of Q, to make key recovery possible.
I think this is really interesting! P2WPKH has a useful property which Taproot lacks: a held coin does not reveal an EC public key, so it cannot be stolen by a quantum computer until the owner tries to spend it. P2TRH brings a similar property to Taproot.
Another idea to build on top of P2TRH is relative expiry for the key spend. After, say, 1 year of holding, a P2TRH coin becomes script-path-only (the key spend is disabled). In case of Q-day, the holder has a fallback without relying on the EC-disabling fork: wait until the EC path expires for that coin, then use PQ script path. This should be safe even if quantum adversaries are fast enough to steal from the mempool.