I don't see any reason to hand your private key over to the SMPC, the point of this thread is that our transaction design is already such that users can separately sign a transaction. You could use SMPC to build the transaction to sign, and then everyone signs.  This would be less brittle, e.g. sybils don't get your private key they can only jam the process or get a user unfairly banned. OH you say that at the end.

I don't follow why you think you need signature privacy at the end? You could use a homorphic mix, or just use SMPC to do the combine (e.g. two phases)... but the signatures only show ownership of an input, and the input side is normally not considered as private.

I'm not aware of any general production scale implementations of SMPC, it would be very exciting for a lot of things— are you aware of any system that could be realistically tasked with signing bitcoin transactions with commodity hardware separated by consumer internet connections?