I had something similar. Although the vibration wasn't bad. I could feel it on the steering wheel. It didn't pull toward any direction. I had them check the drive shaft and all the possible wheel problems. No answers. I asked on the boards and still no fix.
Then one day I was talking with and old time mechanic and he asked if it did it more when I was going slightly up hill and the engine was working harder. I told him yes. He said it sounds like your missing a plug. Sure enough, a bad spark plug. Fixed it and problem solved.