I Googled that model and it looks like the model Deere that has the same rear frame as an older 500 series Toro. Horizontal crank Kohler driving the pumps under the seat with a multigroove belt. Basically the same engine plate as the Toro from just under the seat on back to the rear. I would check their dampers out.
The good thing is that the damper only provides some resistance to handle movement, to both keep the mower from jerking and to keep from damaging the pump.(Quick movement of the control handle causes the rotor in the pump to blow/jump off of the wear plate which in turn causes the case pressure to rise and possbly blowing one of the case seals.)
It probably would not have to be the exact damper to improve operation.