I know you said you checked a lot of this stuff, but bear with me as part of this is me "thinking out loud"..
When you talk about turning off the gas, the idle jets are the first to go without fuel, being higher in the float bowl than the main jets. If the bike runs better without the idle circuit, the jets might be buggered a bit so they are bigger than what they should be (the PO on my bike decided to drill them out really big, for some reason...), the idle air passage might be blocked or the screw is in too far, the floats are not working/ incorrectly set, or the upper end of the jet needle might be slightly worn, allowing more fuel to slip past.
From my experience, the keyster kits are OK; the gaskets are good and the main/idle jets seem to be a good match. Some folks have had potential issues with the float valves, but mine have been fine. However, the taper of the jet needle provided in the kits is different than the OEM needle. It's skinnier on the top of the taper, causing the bike to run rich at lower speeds and eventually fouling the plugs. The OEM needle jet kits are still available from Honda. It is listed as: Needle Jet Set (Needle Jet, Jet Needle (KeiHin #27201) and E-clip): 16012-300-014 and runs $16.28 each. I like this better since you are replacing ALL the parts prone to wear. Floats are still available from NOS suppliers like CMS or David Silver Spares.
A thought, if you pull the carbs apart again, look at the number on the jet needle. You should see the funky "K" (keihin) logo and the number 27201. If it reads different, someone might have put aftermarket parts in, which could be your problem...