Bioshock Infinite: A Possible Songbird Explanation

     Spoilers ahead.

     Throughout Bioshock Infinite Booker and Elizabeth are chased by the entity called Songbird.  Evoking the Big Daddy and Little Sister relationship of the earlier Bioshock's, it made me wonder- who is in the Songbird?

     One clue is a Voxophone recording of Jeremiah Fink left near some design blueprints:

A Child Needs a Protector

These holes have shown me yet another wonder, though I’ve yet to see the application for it. They illuminate a merger of machine and man that is somehow the lesser, yet the greater, of both parties. The process seems to be irreversible. Perhaps, though, Comstock will have some need of this kind of thing to keep watch in that tower he is building.

     The implication being that Fink may have seen Big Daddies and based the Songbird on it.  Furthermore, if he did use another being in it, why was it so protective of Elizabeth?  (I also like the Big Daddy and Little Sister in the background of the scene of Songbird's death)  It would be worth mentioning that during the death scene blood comes out of the Songbird- see pic above.

     Here's what I'm thinking- mind you this is kind of far fetched- it is based on complete guesswork.
     Considering the path Elizabeth is heading in through the Burial at Sea DLC, becoming a violent protector of alternate versions of herself, maybe with her vengeful path she either puts a Booker or Comstock in the Songbird...
     ...OOOORRRRR...
     ...what if she puts a version of herself in it as a punishment?  Cage-ing the bird.  She does wear the bird and cage necklace- that I believe at one point during Infinite is the opposite of what you chose earlier, then returns shortly after.  I could be mistaken on that though.  (I would also note that it could be a creator's oversight- but NONE of the Elizabeths at the baptism are wearing the necklace.)

     Granted the Elizabeth in the suit theory is highly implausible, but a Booker or Comstock from another time or universe would be highly possible.  Anyways, this is just me thinking about the Bioshock Infinite game, and possible connections to the DLC.
     Then again, would Fink have let on if he had help from another Elizabeth?  He was essentially pilfering tech from other universes... then again, with Comstock's resources he may have found another interesting person to fill the role for Fink.
     I don't know- there are a few paradoxical issues I have with the end of Infinite anyway, so I'll post more stuff about this later.