If the idle air bleed screw has to say all the way, I would suspect some foreign material blocking the pilot circuit somewhere.
Or there's an air leak at the PAV tube, or perhaps a failed/eaking PAV unit.
You can eliminate the PAV question by temporarily plugging the hose connector on the intake manifold that leads to the PAV, so that the PAV is removed from the intake system, and the hole at the manifold is plugged and doesn't draw air into the intake manifold from that hole.
Then, if things begin to change, the PAV is suspect.
For blockage in the carb, it would have to be cleaned out well, and see what happens.
I've set up a few different types of carbs, and I find the OEM carb is one of the easiest to set up and adjust, so it should be easier than a totally new carb setup to get working right.
I still have the OEM carb on my bike, and I've been able to adjust it to handle a wide variety of changes, and it responds.
The OEM carb really isn't a bad carb. It's basically just like a Mikuni.
But if it gets dirt lodged somewhere, it doesn't work right, and that does happen from time to time.
One thing that's important for a steady idle, is to adjust the screw settings after it is warmed-up. Because if you adjust it when it's still cold immediately after starting, it makes the idle want to drop off and die when it's warmed-up during your riding.
Sometimes that means you might have to babysit the throttle for a minute or so during warm-up, but it should be stable when it's warmed-up and you're riding up to a stoplight, and shouldn't die-off when it's hot.