I'd be okay with an alternate Borg origin in general, as in just presenting an alternate like people did for a while before Destiny. But not with having two different origins within the same multiverse, any more than I'd be okay with having two different origins for humanity within the same multiverse.
I think there's something to be said for the idea of the Borg having multiple origins that all converged. After all, their whole deal is to assimilate civilizations and homogenize them into a uniform mass. So it follows that if various different humanoid cyborg civilizations with collective consciousnesses arose independently, then later came into contact and assimilated each other, then the overall whole would converge toward some homogeneous, "average" type of cyborg collective. So even if you took away one of those founding cyborg collectives, the combination of the others might still converge toward essentially the same average.
I'm not saying that's actually what I believe to be the case, but I can see the logic by which one might deem it a valid possibility if one were so inclined. I do count the Strange New Worlds VI Borg Queen origin story "The Beginning" as part of my personal continuity along with Destiny, but my assumption to reconcile them is that the nanotech supposedly invented by the species in "The Beginning" was actually reverse-engineered from a crashed Borg ship or something. Given how limited a reach the Borg were claimed to have in the Vaadwaur's era in "Dragon's Teeth," even though they were said to be much older than that elsewhere, I assume there were times when the Borg were beaten back or nearly defeated and had to regrow from new seeds, which opens the door for alternate "origin" stories that are really more like resurgence stories. Not the same thing I suggested in the previous paragraph, but similar.