... why do you have 1TB of source code (you don't! mandatory hacker snark)
Is git really supposed to be used for data?
Or is this just a git-like interface for source control on data?
Something like git-lfs is the appropriate solution. You need a little bit of centralization.
All that's really needed is a way to mark individual files as lazily fetched from a remote only when needed. LFS is a hacky substandard way to emulate that behaviour. It should be built in to Git.