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I have a Honda GXV620 20HP GJAGK-1013926 QAF* on a Hustler Fastrack 54". It runs rough. I turn off fuel and it will run, very rough, but runs. When fuel is on it runs, but sounds deep. It is blowing smoke bad. I have put on an OEM carb and replaced the fuel solenoid and it's still happening. I have to change the oil after almost every couple hours because it's just full of gas and I don't want to blow the engine. What should I try next? Rings? Gasket leaking somewhere?

I couldn't tell from the video, but does the mower have a fuel pump?
It would probably look something like this,
It's rare, but the pump diaphragm can wear out inside and get holes in it, which can then allow gas into the air pulse line that leads back to the crankcase, or wherever it pulls a vacuum from on the engine.