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It sounds like you have done a lot of good diagnostic work so far. My thoughts lead me to the fuel line itself. I have seen in the past where it will deteriorate from the inside and cause the flow to stop. Since you have checked the tank and removed the fuel cap, I think that is the only remaining link.
Let me know what you find,
That is a possibility. I was under the impression you had removed the fuel line and found the fuel was not coming out. If the hoses to the carb are accessible, I would remove them and check if the fuel flows when it stalls. If the fuel flow is fine the floats would certainly be a good next step. Possibly some tarnish has gummed up the float or a passage and only shows up when it is hot.
I believe I have to select final answer on my end. Thanks for choosing Just answers and good luck with the mower.