OK, about the thumping and vibration. It should be fairly obvious if there is something wrong with the driveshaft....look for looseness, side to side play, bent shaft, binding, wobbly wheel....etc.
Also, look at the pulleys used between the motor and grinder, they need to be tight. Die cast pulleys are inherently inexpensive, out of round and out of balance. They have cause these types of complaints in the past. The solution is a premium set of cast iron, machined and balanced pulleys that run true and smooth.
Phil made a very good point about the controller settings. There is a trim pot inside the DC controller named "IR". This controlls how fast the controller responds to loads. If it is too sensitive, the motor performance may be erratic at times and will surge, lurch and jump around at various intensity depending on how extreme the situations are. Basically the controller is over-compensating to loads. It runs smooth without the belt as expected, however, the belt(load) seams to highlight the problem....this kinda points to this adjustment. Try turning down the "IR". When it is turned down too low, the grinder will lose speed under load and will be sluggish to recover. This is an adjustment that you tweek under power to find the optimum for your situation and preference.
I leave belts on my grinders all the time...I'm too lazy to take them off...and really don't care about wobble. Mostly, I use the face of the belt...not the edges. So it is no big deal to me if the belt wobbles. If you need true running edges, (most of you do) ...take the belts off at night.
As far as grease for the drive shaft bearings. I had a very interesting conversation with a bearing engineer about this. The jury is still out, but his recommendation was "never lubricate the bearing...period!" He explained that rolling element bearings don't need lubrication since everthing is in rolling contact...and not sliding. The problem is that too much lub in the bearing causes the rolling elements to "skid" rather than roll. They hydroplane under very light loads and high speed as the balls plow through a thick goo of grease. When they skid, they scratch the surfaces. With this idea...he stated that in tests, a completely dry bearing will last longer than an over- filled bearing. Hmmmm....I would have never thought this. So, I never lube them even though this is against what normal logic tells me.
-Rob