On the Re-Birthday thing, I think that is IS Allen...'s 'split'. It seems like all the Lens are split from each other- Behemo->Hansel->Pollo->Allen->Irregular->Punishment, all alternate selves/outcomes, almost like alternate universe selves, but all in one world. They also seem to be literal splits in that they get progressively dumber. HOW this happened I haven't a freakin clue. An unlikely theory I know, but hey, with Irregular involved nothing will make sense....
I disagree with the splits theory, or at least your reasoning for it. The relationship between (some of) these various Lens is explicitly made clear in the series.
Behemo is, first off, not a Len. He may be voiced by one but in terms of character design he is distinctly not (and mothy said that OSSCE, the album with him and Levia on the cover, is the first album without any VOCALOIDs on it, meaning he doesn’t consider them VOCALOID characters either).
Hansel is the product of an experiment that was trying to create a suitable body for Behemo, and (supposedly, although I can’t recall where this was said myself), he has a fragment of Behemo’s dragon body inside him. This explains his relationship to Behemo. They are two separate people but one was modeled off of the other physically (somewhat–it’s commented multiple times that he’s not a perfect clone). As for Pollo, he’s just a reincarnation of Hansel. They are the same person. That is their relationship. As for Allen, as I understand it, he is descended from the Lucif twins, which are, again, the product of an experiment creating a body for Behemo. He has no relationship with Hansel, but as they (sort of) come from the same source, they are identical in appearance.
As for the others, most of the information on them recently was in SCAP, which I haven’t read. I do know that Punishment is explicitly a result of refining the soulless “boy” in the graveyard into a weapon (Punishment and the “boy” are not the same being, however, because he’s still down there while Punishment is being used).
There could be some form of “alternate selves” going on here with Irregular and Allen but I’m not getting any precedent for it if there is.
I also disagree that they’re getting dumber. Hansel seems to have a consistent intelligence level, Allen is certainly not dumber than Hansel, and Irregular seems to be from all accounts more of a blank slate than anything. And Punishment is just a weapon.