Very interesting theory! Though there's a problem with it: had Ivy not kicked Croc out of the chair, Batman never could have replaced him. So the sting relied on Croc, at some point, leaving the table. That's too much to risk to not replace him before the card game.
Also, Timm mentions the guy getting tossed in the background, but he never says that's when Batman becomes Croc. Maybe he does elsewhere, in an interview or a book, but not on the commentary.
Welcome to the boards, by the way!
Thank you! I just liked the idea, but never really thought about the kicking the chair out part...But my answer to the problem is...he's Batman, he would have thought of something else