> It seemed reasonable to me record the deployment history in the repository

That doesn't seem reasonable to me. You'd be using Git for persistence concerns that are not directly related to source code management.

"Environment X had commit a1b2c3d deployed at 1970-01-01T00:00:00Z" is all you need to store, and I don't see why you'd want to do that in the repo itself. Commit a1b2c3d exists regardless of where or when it's deployed.

Store that data in the thing that handles the deployments.