Although the above sounds like a fuel problem, it also sounds like an overheating problem. If you haven't removed all the housing to reveal the fins, please take a look. What I found under mine was a nice varmint nest. Just enough stuffing to let the engine run for about 5-10 minutes, then a shutdown, followed by a cooldown and start again. And yes, I did initially treat the problem as a fuel problem and totally cleaned the carb, checked the fuel pump, lines and gas cap. None of those fixed the problem; but cleaning out the fins (I used a power washer, but that was over-kill) had it running until I shut it off. Don't feel bad though, all those things you've already done, need to be done occasionally.