First, the air screws shouldn't be out two turns. You are compensating for another problem. The problem very well could be electrical and not carburetor but there isn't any way to tell with the lack of info.
What type ignition do you have? The problem with the strobe light indicates that your coils are not firing all the time. This indicates ignition problems. Since you are sooting the #3 plug and the ignition problems seem to be on 2 and 3, I suggest you look at fixing the ignition problem.
First, if you have points/condensor, get a new set of points and condensors or as Loud pointed out, spring for a Dyna S. The prices on those things are incredibly low at this point. Try Z1enterprises. Also get a set of Dyna plug wires and some new coils. If you still have the problem (and I would be surprised if you do), move the discussion to the carb forum area.
I know it is a bite to spend the bucks but if your ignition is bad; and that includes plug wires/caps and points/condensors, the bike just won't be any fun to ride.
If you were sooting up the #3 plug and did a plug chop correctly; that is, took the bike to a desserted area, stopped and swapped in new plugs and then immediately took off and ran wide open for 1/2 mile and shut it down with the kill switch and looked at the plugs, the ONLY way a plug would soot is you have a MUCH larger main jet OR an ignition problem. The airflow can't be obstructed as your slides are open and air is coming through the MAIN VENTURI. It IS possible that the main jet you are using is hosed and someone drilled it too large but if your #3 plug soots during normal riding as well, it isn't likely that mid-range and idle circuit are both way richer than the other carbs.