Have you run git fsck? It should tell you what kind of an object is missing -- and might say who pointed there, I can't remember. Regardless, that's the next step to figuring out who points to it.

For this:

> I've cloned the repo again, and that object does not appear in the new clone, so I assume it must be from a commit to a local branch.

I hope you realize it can be within a pack, not just as a loose object. git cat-file -t 1cae71a9d5b24991c0d632b45186ca8a250e5d52 in the other clones.