Mystery vibration at 25 mph can't be diagnosed. It's not the front end!

Had a '64 Chrysler limo once that shuddered right after take-off and then at expentional increasing interval speeds.
B&T unit was already changed to u-joints adn I had the axle shaft balanced already. No help.

Turned out the transmission mount was totally mush and soft by being soaked with oil over the years, which let the transmission try and "work itself around" the driveshaft centerpoint.