its a 65 with original transmission tels me it has ball and trunion type driveshaft.....i just went thru this with the waggin...made the dash shake like crazy...changed out the driveshaft and she's smooth as glass now, that the only thing left that could cause this the way you are describing it, hope this is helpful, for a test remove the drive shaft completely and run her thru the gears...shut down the engine in gear because she wont go into park till the engine stops.....
