You’d still need to OTS it though since an attacker could do exactly the same with establishing the threshold.
I don’t think you can get around requiring ordering if the source of truth is the key in question.
That said, we have a pretty secure source of time ordering and OTSing is quite simple, cheap, and you only need to verify it under a very rare circumstance 🤷♂️
I'm not sure if you understand what I'm saying, it's just moving the ots proof and creating an additional layer of abstraction so that uX would be better imo. right now I believe your proposal means if someone gets compromised they have a minimum of x amount of time before you could migrate.
The suggestion I'm saying is to bake that in ahead of time and make migration fast if compromised.
also in the case your new key were to get compromised before migraine, this would help with that, since you aren't pegged to a specific new keypair