I also have the 422 but with the Robin engine. Over the years I have done several mods and they have helped out a lot. First, I insulated the fuel lines and this helped with vapor lock. Then added a fan to the side of the engine cage to pull heat out of that area and taking temps of before and after this has shows this also helped a lot. Also modded the exhaust manifold to eliminate the 90 degree turn in that pipe to a a smoother turn into the muffler which again has helped with heat issues. These days the only time my PT shuts down is if I run out of fuel, maybe I should replace the operator?
I too have a few steep hills, I try to mow then while the oil is still cool, helps a lot with traction. I also mow these areas backwards again helping with traction. You stated after running 3.5 hours you have issues, is that continuous mowing for that long? If so, you are creating a lot of heat in the engine bay and I would suspect vapor lock. These days I try to keep mowing under 2 hours continuos and then let it cool off before resuming any cutting, esp on hot days. After 2 hours I need a drink anyhow.