Run and stall sure sounds like a fuel flow problem to me. Ima few years behind you but still able to do a lot of things I expect will be more limited in a few years.
I would remove the fuel tank, and check the outlet fitting for debris that can get drawn to the outlet by fuel flow and restrict the flow.
You could test the theory by using a portable IV style fuel feed direct to the carb fuel inlet. If it quits its misbehaving it might well have some junk in the tank, so to speak.
Seems to me, unless there's a lot of gunk in the sump, sludge style stuff, the CR should work pretty reliably, and it has for umpteen years. (I am apalled at $800 for a cam swap) They generally don't flip flop too much, and when they fail it is a broken bob arm that removes the weight that allows the CR to quit dumping compression. Sometimes it eats the cam, etc, and you get to replace the engine/etc.
Any way, I would try an independent fuel supply, after checking that the float moves freely inside the float bowl. A partially sticking float could deny fuel flow, then after sitting, drop, and allow fuel to refill the bowl, and off you go again. My old geezer mower seems to suffer from vapor lock on hot days, causing the pump to push bubbles to the float bowl. Once it gets hot, I have to remove the hood, and sometimes that will make it run properly, sometimes it will gargle on with disturbed fuel being ingested, and it does not like that. Solution? I will run the fuel around the top of the engine rather than across inside the blower housing.
Check your fuel supply situation.
tom