The diff bushings will have nothing to do with handling. When they go out you will have a clunking on acceleration and deceleration.

I don't agree with replacing everything. Simply raise the car safely with the wheels suspended and use the 4 P's; Push, Pull, Pry and Prod on all the suspension members and replace the loose ones, then do a four wheel alignment. Replacing dogbones that are still tight is money wasted.

Good luck,