I've just bought a secondhand MKH 416 with the same problem. It looks like its a fair bit older than the other I have so I'm guessing its a common wear and tear problem. It was also a couple of dB lower in level. The level issue was fixed by recalibrating the louder one down since both were at the maximum and to fix the XLR issue, I cut out a few bits of plastic packaging - the thin but rigid type - in about the same shape as the circlip that holds the socket in. I placed these under the circlip and it wedged the socket in nicely.
None of the screws I found actually had anything to do with holding the socket in. The one that goes straight through the body is to hold the casing in place whilst I couldn't figure out what the smaller one inside was for. Neither are reverse threaded. I had tried to take the XLR socket out completely but it would only come out so far. I suspect that the wires were too short and holding it back and that I may break them if I continued so gave up with this.
Bottom line, if you can get the circlip out (its a bit tricky without the correct tool but can be done), packing it out underneath seems to have worked a treat.