Like Bryan I suspect driveshaft. Is it possible that when the tire blew a tread belt wrapped around the shaft and bent it a little? Even if it later came off. Look for drag marks on the shaft. Also, at least with some vans, if a shop lifted it on a frame lift, the rear axle could drop far enough for the driveshaft to drop into contact with the head of the lift. That could dent or bend the shaft.
Has anybody removed the driveshaft? From what I'm told, the sections should NOT lie in a straight line. A slight offset cancels vibration. If perfectly aligned, the sectional shaft tries to vibrate as a long one-piece might.
Oh, a driveshaft shop found one of our shaft yokes was not welded true into the shaft's tubing. They cut it out and welded back straight. Smoother!