Well, it works, finally.
I had major issues getting commits to work. Eventually I figured out that git-svn does not send hashes of the files as all other SVN clients that I have tested so far. I was focused on finding corruption much earlier in the game, and drowned in the details.
I am not sure why it is committing a single change twice, but it is showing the same behavior on standard SVN servers, so I think that I am fine.
And here is the final test: