Going to leave this here for next time I need to push or pull to a git repo that's blocked on a network. In my case it was a self hosted Gitlab server.
I've got an SSH tunnel setup through PuTTY running on port 1234. Run this before pushing.
git config http.proxy 'socks5://127.0.0.1:1234'
And then this after to turn it back off.
git config --unset git.proxy