We assume TH350/400 automatic trans?
It's not in the trans, unless it's the tailshaft bushing. Trans should have made noise or come apart after a few passes with that much shaking. I bet the driveshaft or ujoints are damaged, the Ujoint angle is wrong or the driveshaft is bottoming out. It could also be the tires out of balance.
Back in HS a buddy had a '72 Mach 1. At about 90 MPH the car would suddenly develop a violent vibration to where you couldn't see anything in the rear view mirror. If you stayed in it, the car would smooth out at about 98. We never did chase it, but I always felt like it was the U joints or the tires.
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I could explain all this to the girl at the parts store, but she'd probably call the asylum.
White '67 LeMans 407/TH350/Ford 3.89... RIP
Red '67 LeMans. 407/TH400/Ford 3.25
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