Instead of increasing the idle jet, try instead raising the float levels. Typically, today's fuel metering needles are MUCH too stiff (if they were replaced since 2002 or so), which results in low fuel level in the float bowls. I run them at 24-25mm (one float at 24, one at 25) if I am forced to use the new float valves, just to get the low-speed jetting correct. This won't have a lot of effect above 5500 RPM, but if it does then you can modify the needle clip position for that.
The idle circuits in these carbs are not terribly efficient, being such a tiny air passage and jet, and their full adjust range from non-working to working (and back) is 3/4 to 1-1/4 turn: going beyond that either way closes off the dynamics of the air flow (in) or fuel (out), so you're then trying to work in a range where it doesn't. You may also want to either thoroughly clean the little emulsifier holes in those pilot jets or, if they are the ones we (again) get in the modern kits, add another pair of holes. I have also lately been flaring those holes (there should be 8, BTW) with a sharp countersink on both the pilot and main emulsifiers, because it seems to help aerate the ethanol a bit more.
The ethanol is increasing this phenomenon at the very range where you are working: for a test, see if you might be able to find some real gas somewhere for a tank, for comparison. You might be pleasantly surprised!
