We've got the equipment at work and I've made similar board repairs in the past, so I'm not too worried about that part of it.
Thanks for the pointers; unfortunately no, that part doesn't seem to be available on DigiKey. The 1.65mm ID / 5.5mm OD combination is a weird one, and the only one with that combination on DigiKey is a Singatron Electronics 2DC-S006-I05-ND, which is a 3-conductor design, not 2-conductor, and has a totally different board mating interface. A quick browse through of the pictures and descriptions on digikey.com doesn't show me anything that looks remotely similar.
I'll look at it again, and might try something similar to what you describe, but unless I can find an identical replacement part, something tells me I'll be taking the connector off, soldering on a pigtail, reinforcing it somehow, and using an inline connector instead.