There are 3 one way check valves on your truck. Every tank has one except the wet tank. I would check those out assuming the things you listed above all checked out. One of them could be hanging closed under regular pressure drops. Then, when you drain the tanks, the pressure differential is larger which causes it to open. Once pressure is built up, the differential is less and it hangs closed, until you drained the tanks again. Just a theory of course...but there have been problems with them before.
This is what they look like. Part# KN-23000 is a pretty common number for them and should easily cross if you need to. They're a very simple valve, block off plate and spring, but they can stick.
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One is on the driverside behind the step as seen in the picture. That is the air filter canister on the left in the photo for reference.
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The other two are on the forward end of each tank on the passenger side behind the tool box. Both can be seen in this picture.
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The other thing I would do is install an independent pressure gauge before the gauges, valves and tanks. Maybe the govenor is not able to see a pressure drop, which would cause the compressor not to cut in. Just another theory, but checking pressures in other parts of the system might help you pinpoint the problem.