Maybe check the BVSV deal that runs the AAP? It's in the middle of the intake side of the head. I was looking for a good one for a guy and I went through 3 or 4 before I found a good one. They can go bad and not shut the vac off when they at supposed to causing your AAP to be on when it should be off.
Other than that the symptom sounds just like when I have had a bad fuel cut solenoid or bad supply to the fuel cut solenoid. Check the solenoid for a click on battery 12V and check the lead that sends power to it.
Definitely worth pulling the top off your carb and checking the float level with a ruler and setting to spec just in case.
One other thing, your fuel pump might be slightly gimpy or your fuel filter plugged up. All the aftermarket mechanical fuel pumps are garbage these days.
Check for vac leaks with a can of carb cleaner, starting fluid or propane.
That's about all I got and I think the other fellas all ready touched on all that.
I would certainly encourage you to stop buying the national carbs though and find an aisan to rebuild or get a weber. I have dealt with both the 22r aisan carb and the 32/36 weber and I like them both. You mod the aisan to work better for street performance and you mod the weber to work better off road.