The exceptions are look like a client abort. Could you try to do the push directly on the server which runs scm-manager, just to be sure it is not a problem of a network component. Do you use a reverse proxy?
Pushing from the same server as scm-manager (straight to the jetty port) got me "abort: HTTP Error 403: Forbidden". I'm sure I have the correct credentials though, since I've just used it to clone the repo.
I've also confirmed the group my user is in has write permissions to said repo.
Had a very similar issue after converting Mercurial repos to support largefiles. Just as mentioned above, push to imported repositories failed with 403 forbidden and 'unable to handle Mercurial request' in logs. However, a newly created repository worked alright.
After reading this thread I checked hgrc files in repos and they were actually missing in converted repositories! Not sure if it's an lfconvert issue or caused by some import error.
Anyway, copying hgrc from newly created (via SCM Manager webface) repo to imported ones fixed the problem - it actually contains push permissions.