I have had people bring in mowers that refused to start in the spring due to too much stabilizer. So follow directions! Dry carbs tend to flood the engine in the spring. So keep doing what you have been doing.
Over the years the gas formulation changes and is not good for diaphragms and other rubber parts. Floats are the way, IMO. Possibly affixing a suction type carb that does not have a diaphragm will work???
Perhaps the new switch is defective or the wiring is bad. The kill from the reverse is working so tie into that wire with another toggle or push button switch back to ground. Or get a wiring diagram for your model # and track and test each wire and component.
The only thing I can come up with is maybe a leaky porous casting around the intake valve or the intake manifold itself.
Carefully see if one cylinder is running much cooler then the other. Or use an infrared thermometer.
The cool cylinder is most likely where the issue is.
Reading more comments...
In my experience that happens with small trimmers and blowers, ect. The opposite is what I see. The engine running creates a vacuum and quits from fuel starvation.
What about a mulching blocking plate? If used in hi grass that may cause that. Also check that the blades are not up-side-down. Sharp edge must be lowest!