If you have a VPS that's always running, you can just use it as a git remote through SSH without moving things around or any third party software, just put the Git repo on the VPS and clone it via "git clone ssh://user@host/path". You get authentication, encryption and synchronization out of the box with just ssh/git.

Had to vouch for your comment, not sure why it was marked as dead.

Definitively the easiest way to approach this, and the most standard way too. If you already have ssh, which I'm guessing you do if you managed to setup syncthing on it in the first place, then you can literally just point git to host+path and it'll use whatever ssh authentication you already have in place.

Can hardly get simpler :)