Oh, so the socket is the main board, and the header is the LCD? Ah, so then the last picture is comparing old and new? (This would've been more obvious with captions..)
Yeah, you aren't going to find something commercial to shift the centers. Best bet, interposer board, with SMT pins (could use an SMT header and pry off the plastic body after soldering), and the LCD connections will have to be SMT pads, soldered through the header holes (the solder equivalent of a plug weld joint). Barring that, just wire it one at a time, ribbon cable would be alright, or loose wires. Preferably thinner wires (28ga wire wrap style?) so it doesn't get too in-the-way.
Bonus points for wiring to a header, as a top-side plug? Mind the reversed pinout of course.
Tim