Unplug it don't run if it's "fire hot". If you do this it's just going to melt the last one and you are literally playing with fire.
Best thing would be to find someone who is able to solder decent, and have them put a new PCIe plug on the melted on. If you cant find local might ask on board. But don't run it "fire hot" unless your just looking for trouble.
Like I said earlier. I went down to one plug on both boards. The other side front plug and wires are room temp to the touch, the already melted side was hot. What is a reasonable price to pay for another board in us dollars or BTC? I have had a couple message me and want me to make offers.
I had another guy in my ltb thread say something about the ground screws and springs but not sure what he ment.
A new board will cost almost half of the units current price. They are not cheap to get Going down to 1 and it being fire hot is bad, stop it right now and find solution.
Most likely if you can not solder find someone in services or someone who is known to do it and ship your board to them to have adapter resoldered with new adapter. This should be a decent amount cheaper then buying new board.