Well, when a chassis/PCB mounted female connector is broken, that's a definate sign of abuse.
What you've got to do is think business. Is it worth fixing or simply trying to find another?
Bridging ground on the XLR-type conenctor won't fix the other issues. It also doens't affect TX -/+(pins 2 and 3) because Pin 1 is a shield. Nobody should be using shell ground, it's flat out not safe. Shield is not necessary for the signal to flow. It's necessary to protect that signal as much as possible, especially over longer runs. Other than that, not essential for operations.
So, calculate what it costs to salvage it, versus getting running again. I'm all for repairing. Keep in mind these days that we're in a disposable society and culture. It's often cheaper to trash it and replace it than repair these days. This is too bad, I don't want electronics waste clogging up landfills. I'm not some greenie tree-hugger, but I don't like all the deliberate waste that goes about these days.