Not being funny but it could be as simple as the carbs not exactly balanced so that one is running harder than the other......shutting the weak one down wouldn't have as much effect as shutting down the other....
Assuming they are nicely balanced I would remove the idle screws and check very carefully for ribbing on the taper and to see if they are bent.
I had a similar problem and an airline down the hole cured it....I had one barrel that could be shut off without doing a great deal and blowing out the passages cured it.
Good luck!
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