It is possible that all I am about to say has already been covered previously.
I am recapping to get it in one place for myself, to ascertain where we are in the process.
Your statement that covering the air inlet allowed the engine to run on both sides; means you are lean on that side.
Check if you have not already for fuel delivery from the tank. Is the crossover parially plugged going to that side?
Drop the bowl and check the flow and float level.
If you know the carb is receiving fuel from the tank and the bowl is filling properly.
Then have you checked to ensure that the piston in the carb is returning all the way down?
Take the pipe off the carb that goes to the airbox.
Watch the piston go up and down while you blip the throttle to say 4000 rpm.
Is it returning all the way down when the rpms return to idle?
Eyeball both sides to see if they are behaving the same.
If you checked the diaphragms did you make sure to reinstall with the little tabs located correctly.
Having it improperly oriented could cause the piston to stick in the up position.
Also the spring may be buggered up in there causing the piston to stick open/up.
If the piston on the side with the problem is not acting the same as the side without the problem we are narrowing down the cause(s) of the problem.
Most important to me when diagnosing a problem is to start at one end of the system and check/troubleshoot untill I find a point where things are not as they should be. Then figure out why its not as it should be.
The problem must be identified, then the cause of the problem identified, only then can the proper repair be identified.
"Really quite simple Watson;" "not."
At work we refer to this as:
1. Complaint
2. Cause
3. Remedy
HTH
Troy