The one in Destiny is as good as any that for no particularly good reason requires the Borg
. That said, it's pretty well done.
There's a few flaws in that theory, one being that the Federation were still using nanites in the 24th Century (can't remember the TNG episode's name, but it's the one where Wesley was experimenting with nanites, and they ended up trying to eat the computer core).
Another is that Starfleet's transwarp project failed, though one could say historical revisionism on Starfleet's part could have something to do with it.
The biggest problem with the OP's theory is that the Borg existed at least as far back as 900 years ("Dragon's Tooth" [VOY]), so they can't have originated from the 23rd Century.