Agreed, the carb that is overflowing has float issues. But if it ran fine and then recently started doing this along with the overfllow problem, then its probably the neadle and seat assembly (which the float opens and closes allowing more or less gas into the bowl) getting hung up. This would mean its time to disassemble the carbs and give em a good cleaning or replace the neadle and seat if you cant get it to opperated properly after cleaned. As a temporary fix when its overflowing, give the faulty carb a couple good taps at the float bowl with the butt of a screw driver or something as this will sometimes knock it free. You could also try removing the brass mixture screw you mentioned and filling the float bowl with carb cleaner and letting it set overnight, then drain the bowl and see if some of the crud comes out. Make sure you bottom the mixture screw out, counting the turns, before removing it and dont loose the little spring behind it. Then when you reinstall the screw, bottom it out lightly then turn it back out the number of turns you counted when removing it to set the mixture again. Good luck and read the FAQ on carbs.
