Did you try messing with the main idle adjuster? My '87 ninja 750 has a knob on the left side of the carb rack that sets the lower limit of the main butterflies, essentially controlling idle speed. Clockwise = higher throttle, counterclockwise = lower throttle. Turning this clockwise has the same effect as twisting the grip ever so slightly.
Where did you put the idle screws? If memory serves right the 600 is 1.5 turns out. You did take this screw out along with the oring behind it before putting carb cleaner on the carbs, right? If that oring is cracked it will mess with your idle, but it wouldn't mess it up as much as you're describing.
I think your most likely problem, though, is that the cables are too tight. Where the throttle cable attaches to the carb, you can set the cable's slack with a nut. Make this obviously loose. I say this because you said that forcing the throttle closed (which uses another cable that you have to make sure also has enough slack) affects the idle. It shouldn't.
Also, make sure the whole cable is greased. You can get cable lube kits at auto parts stores where you plug up one end of the cable and shoot lube in until it comes out the other end. It worked great on my throttle cables which needed it after 17 years, like I bet yours do.
Where did you put the idle screws? If memory serves right the 600 is 1.5 turns out. You did take this screw out along with the oring behind it before putting carb cleaner on the carbs, right? If that oring is cracked it will mess with your idle, but it wouldn't mess it up as much as you're describing.
I think your most likely problem, though, is that the cables are too tight. Where the throttle cable attaches to the carb, you can set the cable's slack with a nut. Make this obviously loose. I say this because you said that forcing the throttle closed (which uses another cable that you have to make sure also has enough slack) affects the idle. It shouldn't.
Also, make sure the whole cable is greased. You can get cable lube kits at auto parts stores where you plug up one end of the cable and shoot lube in until it comes out the other end. It worked great on my throttle cables which needed it after 17 years, like I bet yours do.