You are right that while BLS is relatively easy to implement as a threshold scheme, ECDSA is quite a bit more challenging. This paper (“A Survey of ECDSA Threshold Signing”, by Aumasson, Hamelink, and Shlomovits, see eprint 2020) surveys the state of the art for threshold ECDSA protocols (as of last year). Unfortunately, none of these protocols really satisfy all of our design constraints: they either assume a synchronous network or they allow a single faulty node to prevent signatures from being issued (i.e., they do not guarantee output delivery) or both.
We have designed new protocols that work in an asynchronous setting and which guarantee a signature is produced when requested, even if some nodes are faulty (but we do assume that less than one third are faulty, as usual in all of our protocols). Our new protocols rely on our consensus protocols. They also perform pre-computations that will ensure that when a signing request comes in, it should be satisfied with just a single round of communication (no consensus needed).
We are writing a couple of papers that detail our protocols and their security analysis. We hope to make these public soon!