So here's the update.
I am still having a problem. At this point:
-all cables and drives have been checked.
-I have messed with input settings on fcp- I cannot seem to find the ones that will solve this.
-the camera has been checked and swapped out.
The image is stable in cam.
I spoke with Grass Valley and picked their brains for a bit.
The upshot at this point is that they recommend a canopus with an image stabilizer, like the advc300, which came out appx 6 years ago and DOES have an image stabilizer in it.
I would do this, but I am not sure this will solve the problem... so I am afraid to spend the $ until I can be assured that I should get that canopus, rather than a tbc, you know?
By this point, I will not make my deadline regarding these old videos for my project. HOWEVER, I would like it solved so that I can access these tapes. As long as the sync issue can be resolved with this kind of purchase, I will do it, if it is less expensive than going out of house.
$1K on transfer house, or less on hardware purchase. I'd rather buy the item... then I can shoot with this unit if I want.