Adding shocks will not help. With a rigid frame machine, one of the rear wheels at some time is not on the ground. The torque of both the mower deck and the engine affect the steering effectiveness at the times when only one drive wheel has good traction. It is like flying a small airplane and letting it side slip and stall, as it goes where it wants to go and hopefully you have enough altitude to recover!!!
The inertia in the moving machine must be bleed off by stopping the machine before proceeding down a hill or sideways on a hill and then slow movement must be put in.
Mad Mackie in CT