I have seen this problem with my mower, but it was extreme circumstances. My son put water in the gas tank and oil fil; he was "helping". This tweaked the fuel inlet valve/seat on the float. I cleaned/darined fluids ect. I could go out a day later, and the gas was gone. Well, it was leaking past the float valve, and draining through the carb and into the cylinder, and seeping past the rings.

I could put gas in it, and it would start. But, it would smoke, and surge. I checked the oil, and it was overly full and THIN.

My theory is the gas thinned the oil. The rings did not seal properly without lube, and it blew by, causing pressure in the crankcase. It blew this icky oil mixture up the vent tube, which goes into the air cleaner. this caused a rich condition which caused the governer to back off. As speed dropped, the covernerkicked in again, then backed off, peat and repeat...

So, I put fresh oil in it, and it ran fine. Added a fuel shutoff which solved the issue when sitting. Finally replace the inlet needle and seat....

Have you changed the oil in this motor?

For the most part, it sounds like yours is running lean, and or has an air leak around a gasket or something. It starts, runs lean, the governer compensates, then backs off when rich. Then it repeats the cycle.

When you cleaned the carb, did you soak the body in a good carb cleaner solution, and blow out all those little holes in it. Bet one of those is still plugged...