Eek! You know, careful application of a heat gun combined with some aluminum foil shielding to protect areas you don't wish to heat can do a nice job of removing a big connector like that intact. Just practice on some junk boards first so you can get the hang of melting the solder without warping, blistering or burning the board.
Works well to salvage parts quickly from junk PCBs too. Heat up the board until the solder starts to melt, then give it a good whack and most of the parts will just fall right off.