hi,
well you have another -tested by me when I was doing r&d in electronics pcb manufacturing- method: the solder 'bath'
my boss had some 3kw cooking induction plate (yep, just some cheap one) and he did made something like a solder bath filled with solder, I really don't remember if it was pb-free or not...
we just heated the solder (the rectangular solder recipient was full at maximum with solder) until the solder was really liquid then just put the pcb with the connector needed to be desoldered upside of course and with a good plyer after 2-3 seconds max you get the connector free, you lift the pcb (otherwise you can damage the board) and you can easyili separate pcb and connector
we took off hundreds of connectors from deprecated designs
the only secret is the 'hand' that operates this, just test with some bad pcb's
ok, it will cost you the solder inside the bath (you have this brick of solder trapped in his recipient only for desoldering purposes like this one, and it's lot of solder)
the method is an old-time-one from 80's when we haven't got hot-air top notch soldering stations in small companies or in est-european countries, where ingenuity was necessary to overcome missing quality tools like in west-eu countries
because the heated mass is relly big, it works 100% even with veeeery big stuff like your connector
damage to pcb/tracks/vias is zero if you keep it quick (touching the pcb with the liquid solder, wait 2-3 seconds with the pcb on the solder without submerse the pcb in the liquid, only touching it, testing with the plier if the connector is lifting up from the board and then lift the board and taking out the connector)
the recipient was something like this one
http://superbproduct.com/Solder-Bath-SBPTC-500.html (only the bath I mean, not the heating part)
don't be afraid, if you got this right, you're the boss
best regards, ovidiu