Ok, I'll take a stab at it...
Firstly, bitrot is a term usually meaning 'silent bit corruption'. How serious a problem is it? It is debatable. Typically a sector(s) goes bad and the HDD replaces it/them without you knowing. So for example, an image falls on a sector that goes bad and you get a partially corrupt image or worse, on a ZIP file, you lose the entire file(s) in it since you can no longer uncompress it.
rsync is not designed for the purpose of recovering from bitrot. As the wiki nicely puts it, it is a widely-used utility to keep copies of a file on two computer systems the same. If bitrot occurs, which of the two copies is the correct one? For that you need 3 or more copies.
BTW, on a disk with files that have had sectors replaced, rsync will still work as expected. It read the file and see it as changed. It will copy it just fine. It is only when the sector cannot be replaced automatically by the HDD, because the pool of replacement sectors is exhausted, will it get stuck.
Since you have 3 copies of your data you could stitch something together with rsync to do a deep scan using checksums of all three copies, compare and update accordingly. I do not know if anyone has done anything like that but I think it should be possible.
The best way to go if you are seriously worried about bitrot is to store your files on a ZFS filesystem on your storage device since it provides detection and recovery of bitrot. I would suggest you read up on setting up FreeBSD as a NAS server. Alternatively I recommend you research RAIDZ disk solutions that do the same thing. These, I warn you, would be expensive.
Hope this helped.
PS: bitrot can happen in other ways not just on HDD. Non-ECC memory for example.