Most of the pain here is the typical set of issues people run into trying to make S3 a filesystem as-is, common with S3FS-family approaches.
ZeroFS (https://github.com/Barre/zerofs) is 9P/NFS/NBD over S3 on an LSM. Point stock go-git, or just /usr/bin/git, at a mount and skip the gymnastics. Rename is a metadata op in the keyspace, so you get it atomic on any S3—no Tigris-specific X-Tigris-Rename needed.
Different point on the spectrum, but less square-peg, also most probably much, much faster (it works great on linux-sized repos) :)
Came here for a five-gallon bucket hooked to Dulwich (archiving rain?), Slightly disappointed :)
Go Git and Dulwich and friends are indeed fun tech.