A disadvantage of a HD multi-signature scheme compared to a Shamir's Shared Secret Scheme is the need to back up the xpub keys. There's no BIP39-like encoding for xpubs, they're long, and they're sensitive so you can't just widely distribute them to counter risk of loss.
Is there a multi-signature M-of-N (M < N) scheme that only needs M private keys, thus simplifying backup (and restore) considerably?
In my very rudimentary understanding of Taproot, you can efficiently chain multiple scripts together. Would it work to reduce a M-of-N scheme to a set of M-of-M schemes OR'ed together? For example, splitting a 2-of-3 with keys A, B, C into a script that accepts (A AND B) OR (A AND C) OR (B AND C)?