Do we have any established quantum DH and DSA algorithms that researchers have agreed on using? If not, then picking one would not make sense because it could be demonstrated to have a weakness.
That’s a fair concern, already we have some established PQ standards such as ML-DSA and SLH-DSA albeit I don’t think that automatically makes either one a good fit for bitcoin.
Bitcoin has its own set of constraints: Signature size affects blockspace, verification cost affects node validation, and a signature scheme would likely be included in consensus for decades. Even if there is a standard algorithm, it may turn out to be a poor engineering choice for Bitcoin.
Which makes me wonder if we should first narrow down the requirements Bitcoins PQ sig scheme needs to satisfy before comparing candidates against those constraints