Thank you for the detailed reply.
I now have all the information to do the changes during the weekend.
Still deciding if I'm losing NTC (much easier and clean solution) or use one of the GND pins (if possible without desoldering the socket).
-EDIT-
Without any HW change, I switched the T12 NTC on/off in FW settings.
With NTC ON and after T12 cold tip calibration, I saw around 1ºC (max 2C) deviation from FG-100 clone in 245,255,320,370C.
With NTC OFF and after T12 cold tip calibration (I calibrated the cold tip with CPU at 40C) and I saw around 6ºC deviation, after fooling around with temp. to 400C, suddenly the difference was 12C to the FG-100 clone. Same T12 tip, it's old and well cooked.
These results are based only on a few tries, so no for sure conclusion can be taken with so few tries.
I was now looking for a way to use one GND pin without desoldering the GX12-5 connector and keep the NTC if possible. If to much trouble I would go for the other option, removing NTC and use that pin.
Because PCB is soft, I decided to try to grind around PIN4 to separate it from the PCB GND connections in both PCB sides.
I used a battery power, hand size much smaller dremel like pen (15cm length) and what looks like a carving bit that I have never used before.
It worked much better than I expected, in a few minutes (3 or 5, I didn't clock), also pausing to examine progress and brush dust, the thing carved a perfect pit around the pin and also ate a bit of the pin top. (I don't have any hollow drill bits or milling cutter bit to try.)