Further tie-ins with the first game? [SPOILER]

So, upon finishing Infinite I was looking for tie-ins to the first game and may have found a few. First off, both main character (DeWitt and Jack) both have some distinguishing marking on them. Dewitt's in the form of the 'AD' brand and Jack's in the form of his chain tattoo on his wrist. This could be relevant to the multi-verse theory because Dewitt brands himself to remind himself of what he did in the past and also remind himself of his goals. Could Jack's tattoo be relevant in the same way in that his path is cyclical and that he is a slave to Ryan and 'Would you kindly'. Also Andrew Ryan's tagline in the first game of 'A man chooses, a Slave obeys.' could be related to the Lutece's theory of constants and variables because jack is possibly both a slave and a man in different universes. (He could even be Andrew Ryan in a different dimension but I digress) The idea of a choice is similar to the idea of a variable and obeying would then relate to constants. This leads me to believe that Jack's struggle to overcome Ryan's commands in the first game is similar to how Booker creates memories when none exist. (DeWitt gets a bloody nose, Jack has somewhat of a nervous tick response when Ryan gives him commands which do not align with his current reality.) It has been noted that before Elizabeth kills Fitzroy, Dewitt lifts Elizabeth into the vent in the same fashion that a Big Daddy lifts a little sister into a vent in the original Bioshock. Perhaps, Booker could in sense be a Big Daddy. He is Elizabeth's father/guardian in either universe and possible relations between Fink, Dewitt, and rapture could mean that his actions either inspired or influenced the role of a Big Daddy. This could also just be a subtle nod to the original game. What does anybody else think? Do you think these could actually be tie-ins or is too much of a stretch? -Cheers