I do not want a card edge connector that sits on neither the top or bottom of the PCB, I need one that sits parallel to the PCB board.
I think you are after one these "bottom edge, straddle mount" connector types:
We once used some that went to a 5 x 100 row connector on the backplane, had 2 per board. That was a lot of IO! I don't recall what brand it was, that was back in the early '90s.