Many thanks for the detailed reply.

You just made me realise something - actually the use case I had in mind does require accountability - in fact the N keys must be known and provable at time of locking and the M signers must be known or somehow deducible from the spend at time of spending. So I guess the super-efficient threshold signatures are out of the question.

The tree of all possible signatures seems like it *could* work for what I want to do, although the tree could get very big too.

Would you be able to point me to any resources (code, medium, etc) which explains these trees with more clarity?