in my experience the big Retainer Plastic valve baskets crack and get worn out I replace them with the a valve kit, its expensive though. The valves already come put together in the kit don't buy the basket separate been there done that, and the valve springs wear over time. Had to do my cat 3535 about 3 months ago. Make sure you get two kits for the inlet and outlet valves its 6 all together Top & Bottom on pump head. part#PU34235 from keen rite cost me $524.88
Before i done this I would inspect them nothing is cheap on a cat 3535
1. incoming water like you guys said is good.
2. check/inspect all valves get a huge wrench from Napa just for this for leverage.
3.I would maybe point to seals but sounds like your pressure is goo 1000psi ?
maybe someone else will chime in.
4. Check valve also like everyone else said what kind of automatic do you have?