Am I right in understanding your proposal effectively makes private nonces deterministic, through the sender choosing a derivation path for the public nonce?
My (limited) understanding of Schnorr is that the private nonces must be generated randomly.
It would seem that allowing the sender to “force” the recipient to choose a particular nonce based on the derivation path for the public nonce potentially changes the security model here.
Edit: The catastrophic case would presumably be if the sender somehow forced the recipient to reuse a nonce that had been previously used in a signature. But there may be other more nuanced issues here with deterministic nonce generation.