It seems like it might be either a bent axle or a bent drive line, or something is binding up in the rotating assembly, maybe a bad bearing race or a bearing race that has worn out of true. If it was the tires you should be able to make the oscillation change by moving the backs to the front.
Here's another thought- how are your motor mounts? The front of the torque tube is attached to the back of the transmission, and any slop in the front or rear motor mounts would telegraph right back to the back axle. The angle of the torque tube has enough lever action against the pivot points on the axle to be able to move it vertically slightly. You might try driving with your floor cover off and see if you see the back of the transmission moving around with the oscillations you feel.
