In my experience (which is mostly M:S but now also DT2) if you’re only renaming and moving to different folders, the hashing thing should work. (Cases where it won’t work include things like if you expect a sample and a re-sampled version of it be treated as the same thing … they won’t … the file contents have to be identical).
That said, I always back up my projects with transfer first in case I do something stupid like miss out a couple of files in the re-organisation. When I’ve needed the backup, it’s always been my fault, never transfers fault. In my experience.
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