it may be a warn bushing in your steering. i had a dramatic shudder vibration at 35 mph only that was set off by small bumps in the road. It was worn bushings in the tracking arm. Took it to a dealer and regular mechanic and they had no idea. Drove me crazy then took it to an alignment shop and they put it on the swivel pads and moved the front wheel back and forth and you could see the play in the bushing. New bushings and no more problem.
You mention the drive shaft joints seemed fine according to the mechanic, but you don't mention if they've been recently lubed. This is important even on good tight joints. For instance, mine have been greased every 10k or so with synthetic grease since it was new by yours truly. Yet when they begin to get dry I notice two symptoms. One is the rear suspension gets stiffer feeling as the shaft splines bind slightly (especially when accelerating away from a stop and hitting bumps such as crossing an intersection), and the other are slight vibrations at certain throttle and coast speeds and settings. Literally an hour ago I lubed them because I noted the other day that crossing an intersection in my neighborhood caused a stiff jarring motion I normally don't feel unless the rear airbags are pumped up for towing.
I agree with Kurt's analysis 100%. Lube the shafts (check the FAQs so you don't overlube the splines, BTW) and swap the tires F/R. The fact that this changes on acceleration puts the shafts as the culprit into the highest category IMHO. Perhaps the PO neglected them?
