So the actual diff moves in the frame or are you just seeing the axles moving? If your diff is moving I bet your bolts were loose and from the toqure of the engine you enlarged the mounting holes. Ouch. If this is the case you'll have to weld some washers to the tabs in the correct locations to stop it from moving. I did this fix to my right upper a arm mount. The previous owner did something and left the nut and bolt loose and it enlarged the hole and my a arm would shift even with the bolt fully tight so I welded a harden washer in the correct position and she's good as new now.