I am going to relate a story, and lets see if it could be relevant . Had a customer from a few years ago that owned a craftsman with a similar V-twin Intek. It would run about like yours and then would sputter, miss, backfire, and eventually quit until it cooled down. All the things that you have done was done to that engine. In the end we discovered that there was no shielding between the exhaust and the carb, and the heat from the exhaust was actually boiling the fuel in the carb. If you touched the carb after it quit, the fuel bowl would be so hot that you couldn't hold your hand on it. And you could hear the fuel in the bowl bubbling.
The fuel bowl should stay relatively cool to the touch.