2005 CVPI Shaking at speed

Hello all. I hope you can help me with my problem. I have a 2005 CVPI that shakes while driving.

The symptoms:
-Car shakes some while driving at any speed; worst between maybe 35-55.
-The shake is the same whether accelerating, coasting, or idling

Things I've done:
-Before the shaking started, I replaced one of the ignition coils due to a misfire in cylinder 3. The problem was fixed. No MILs since, and the current shaking is quite different from what it was doing when it was misfiring. This is more of a cyclical "thump."
-Thus, I got the tires checked out and balanced. This did not solve the problem. They're pretty new, too.
-Had guys check the driveshaft/u-joint (fine), brakes (fine), and suspension (fine). They think that I am crazy and that there is no problem with it, so I don't know how thorough they were. It used to be smooth as butter, though.
-Baby just passed the state inspection, too.

Thoughts on what to check next? I'm not super handy with a wrench yet, but I am certainly willing.

I have no idea what the problem is but you could try this. Raise the rear tires off the ground about 1" using jack stands. Have someone start the engine and put it in drive while you watch the wheels and drive shaft. See if you can see or hear any vibration. Just be CAREFUL!!! Block the front tires, make sure the jack stands are secure and do not let your helper run over anyone. This might give you some idea if your driveline is running smoothly.