Pretty sure I agree that FROST is closer to the mark in what @fiatjaf is looking for, but specifically the signing algorithm and not the keygen algorithm. FROST (and Pedersen DKG before it) were advancing the state of the art by allowing for no central party (or aggregator/dealer) to be in possession of the whole private key at any time, either in key generation, or in signing. Here I guess you want to reset back to the earlier SSS basic idea of having the central party know the key in advance, then construct the individual shares such that they sum to the pre-existing key x, instead of following FROST's KeyGen to generate the shares.

But the "massive caveats" I mentioned in the other post still apply; it seems unlikely you'd want to allow the possibility to collude to take your full key.