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When I come to a stop it feels like the drive train is shifting forward, and when I accelerate it feel like it is shifting back. Could this be because of soft rubber bushings?
The bushings are just there to absorb vibration and stop them from being transfered into the body. The bushings themselves should be captured and not allowed to move more than say 1/2". Higher durometer isolators will transfer more vibrations.
My first though would be axle wrap. You might try it in 4wd to see if it lessens.
I suppose the mounts could have deteriorated or just been a weak batch, but I wouldn't replace them with polyurethane because of the vibration issues. So if they need replacing, I would go back to stock.
If it's axle wrap, then you have a few options. Axle wrap is caused by the torque going to the tires twisting on the springs. The further the axle is from the spring pack, the more torque is applied to them ("give me a lever long enough and I'll move the world"). So if you have a lift kit, replacing the blocks with taller springs. If you don't have a lift, new springs might still help, but you could also add a roadmaster active suspension kit, or ladder/kicker bars, or pretty much anything else that limits the axles lateral play or the springs arch.
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