It really feels like rsync should have a multi-path setting that would have sped this up across multiple links (but doesn't because noone has made it yet).

You could just run multiple rsync processes using different src and dest paths to achieve multiple copy streams. Anyway this would not be likely much faster if rsync is run over encrypted SSH due to CPU performance, compared to unencrypted SMB.

I use bbcp for that, it supports multiple streams.

https://docs.nersc.gov/services/bbcp/