Does the 'rev' field in the metadata for a file change if the file is moved or renamed?

You should not use the rev to track changes to files across moves/renames, and in fact the rev value is always expected to change when a file is moved or renamed. Be careful when comparing rev values by eye though, as subsequent values may differ only very subtly, e.g., by changing a single character slightly.

Anyway, API v1 unfortunately doesn't have a good way to track moves/renames like this. The other techniques one might try are not ideal, as you mentioned.

API v2 will, e.g., by offering IDs for files, but that's currently just a preview.