Thomas,
First, I have always had very good experiences with the service department at both of my "local" Rover dealerships ( Bedford, NH and Scarborogh, ME). I have had them do several major jobs on my truck and a few minor ones that I just couldn't do for one reason or another and I have often called them up for advice and recommendations. So don't take this as dealer-bashing. That being said...
Before you take the time out of your schedule, drive down and sit in a waiting room while someone charges > $80 to look at it and tell you a lot of what you already know, try some alternative sources. I have gotten a lot of my electronic and mechanical parts from Atlantic British and Rovers North ( I don't know your geographic location, but they both have quick shipping turn around ). Both take the time on the phone to make sure you're getting what you need and if you spoke with them and emailed them your pics they can probably find what you are after.
Although I have not used any "junk yard" sources, a lot of other people on the board have a lot of luck with that as well. If you can either track back the wire to the connector at the other end (probably not that easy) or just have a junk yard cut off the plug and first 12" of wire you can probably get it very cheap. This method assumes you are comfortable with making the wire-to-wire connections yourself, but if you can get it for $10 vs. $80 just to have it diagnosed it may be worth the attempt.
Finally, have you inspected the plug really close to see if you can track the problem back to a specific incomming wire that cuases the jiggle-to-fix issue, or does it seem to be the enitre plug? Perhaps you could use an appropriate electronics-safe cleaner on the plug and prongs or an after market product to increase the quality of the electrical connection between the two.
Just my 20 millidollars worth. Good luck!!