So the question that remains, I guess, is whether it is even supposed to work over HTTP(S) or GIT protocols. In the case on hand, I can live with having to authenticate every time I pull or push but for the more general usage I will look at the GitLab appliance...
OK, it *does* work over ssh...
... i.e. using a Linux username and password as well as the absolute path:
git clone ssh://vcs@MYREDMINE/srv/repos/git/<reponame>/.git
So the question that remains, I guess, is whether it is even supposed to work over HTTP(S) or GIT protocols. In the case on hand, I can live with having to authenticate every time I pull or push but for the more general usage I will look at the GitLab appliance...