Forgive me if you have already been this direction, but my brother had given me advise a long time ago about carbs and it seems to always work. Every hole in the carb has a purpose and must be clear. If the floats are correct and the needle is not leaking, the air screws are at about 2 to 2.5 Turns out, all of the holes are clear, it has to work. The test where you covered the air bleed hold and the idle kicked up eliminates all mechanical and electrical culprits and isolates the carbs.
With my Bandit, I had the carbs off and on about 3 times before I discovered varnish in one of the pilots that chemicals would not remove. I had to run a wire through it to clear it out. This fixed it for a few days, but then the problem came back on a different cylinder. Again, in disassembling the carbs, I found a very unlikely source of contamination. I had put a small amount of bearing grease on the needle jet o-rings to aid assembly, it had come loose and been drawn into the idle circuit. The hole is so small that it would not allow it to disolve and be pulled through the carb. Upon cleaning, it cleared up again.
My advice, start over. Disassemble everything under the float bowls, including removing all of the pilots. Clean thouroughly with good carb cleaner and make sure every hole is clear with compressed air. You should be able to see a definite hole through the pilot. Don't use any thing thicker than WD-40 during reassembly. Put your inline fuel filter back on (the smallest flake of rust and you will be doing it again) and you should be in business. Balance the carbs if you haven't already and it should idle and run like new.