Again, this requires you to have a persistent clone on a filesystem. I specifically wonder if we can do (and I quote) "direct incremental git-to-S3 backups", and you keep replying "it's easy, do it indirectly with a persistent cloned repo".

I don't understand where you are stuck, tbh.

yencabulator has provided a good tip I think, as you could store the previous set of refs and use that to build an incremental Git bundle (one with only the objects that were not in the previous bundle). I don't know if you can do that with the existing Git client though.