Ed, that connector has 19 terminals associated with it, not an easy task to repair even if possible. Further, it appears 3DR does not repair the gimbals at all, they replace with new only. They pot all connection in and around the board related to the HDMI cabling (ribbon). So any attempt to repair could result in further damage.
Pyrate's suggestion is really the only option at present.
You could possibly by-pass the connection with some type of homerun connection to the HDMI port off the main board. But I doubt it would allow a free moving gimbal thereafter. I don't think it would be worth the effort and expense.
Beyond the gimbal's connector damage, if the gimbal is physically undamaged, I'd be interested in buying the unit from you. Let me know a price that would be agreeable. I'd be using it as a mock up for my gimbal vibration mod'ing efforts.