Thanks everyone! All very helpful.
In our case, these UUIDs are not references to the file, but to the original physical object. For example, a letter that has multiple sheets might have 6 files associated with it, but only a single UUID. As far as I know, there isn't a way to represent this physical object in the METS - no way to bring together these 6 files as referring to the same physical object - other than in the structMap (we would likely add the same UUID at the file level <div> for these 6 files). I know the GROUPID in the fileSec can be used across the different fileSecs to tie together multiple derivatives of the same file (e.g. jpeg and tif) but that’s not what we're doing here.
DIDL is not an option for us. We use Rosetta (by Ex Libris) which is PREMIS-based and stores all the information about Intellectual Entities, Representations, and Files as METS XML.