Air cut valves? all held vacuum but maybe not working like they should?
They should hold vacuum, but you can test them to verify they open and close the valve when the diaphragm moves. I have found 2 of them that would hold vacuum, but did not operate the valve. If you have a Redeye rebuild kit, he has the tools and instructions for testing them with a mighty vac.
Checking the air cut valves at this point involves removing carbs and taking them back apart.
I would follow Jersey's advice and check for vacuum leaks. If there are no vacuum leaks, or exhaust gasket leaks, maybe try opening the pilot valves 1/4 turn on the cylinders that are popping. That will enrich the pilot circuit and may stop the popping. I am assuming that when you cleaned the carbs, you got the slow jets clean. If the slow jets are blocked or partially blocked it will cause a lean condition. Sitting on the side stand with fuel in the bowls for a long period could cause the jets to plug.
Good luck, and hang in there. You will figure it out.