I have just fixed the problem in mine, I have a few observations. Of course, do it only if you know what you do, I do not take any responsibility if you mess up your headset/fry your computer etc.
Replacing the whole port might be counterproductive: most likely it gets broken off the board, like mine did, so it might be still in good shape. If so, it is much easier just to resolder the pins. Of course, if they are broken off or bent badly, orif the plastic part is damaged, it will not work.
The main problem is this: the port consists of a rather sturdy metal support, which is solidly mounted on the board. However, within it is a plastic part, which contains the plug/board pins. The issue is that the metal support holds the plastic part only with a kind of a bent metal tab, which in time gets bent off. Curiously, it seems it is much worse to push the USB plug with too much force than to pull it. If the tab is loose, then all that holds the plastic part is the solder, which understandably might break off quite easily if the connector is yanked.
To fix it, you need a VERY good magnifying lens or other means of magnification. I have used a cheap USB 40-1000x ‘microscope’ (just a webcam, really). A solder gun with a very fine tip would be quite useful, too, I managed with a regular one. I would say that a well-regulated solder gun is essential, I worked at 260 C. If you get it too hot, the plastic will melt and then it is game over - it is quite difficult to operate at that scale.
Soldering just the two external pins seems to have worked, although the DATA pins also have traces on the board (to some pots?). If you get lucky, it might be that what is left of the solder on the board/pin would be sufficient to remake the connection. It worked for one of my pins: I have put a good amount of flux on the pin, heated it up and it nicely reconnected. Of course, I expect it will be somewhat weaker. On the other side I had to put a tiny, and I mean, REALLY tiny amount of solder to make the connection. Make sure you do not bridge the pins, you might fry your USB computer/charging port and/or the headset!
What I did not do and I wish I did: I should have fixed better the plastic part to the metal mount, but I am not sure yet how. Still, I will avoid charging the set while I am using it…