I have a simple firebase project set up, if you want I can add an API endpoint for you that you can use to upload and download scores. You game is sick so I would love to contribute! And it would only take me an hour or so. I used it for quite a few projects before (including this jam) so I mostly got the hang of it by now. ;p
You can add me on discord if you like (username: bene_labs) and I can guide you