I set the air screw to 1 1/8 turns out for the ride to work (15 miles) and it stalled when I got off the freeway and came to stop signs.
The original complaint was that the bike has a stumble on acceleration.
Did changing air screw position change this behavior?
For the separate problem of stalling...
Do you have you main idle knob set for correct idle speed when the engine is hot or cold?
Do you know the emulsion tube holes are clear?
Do all your spark plugs exhibit the same deposit color and pattern?
Separately, and for the debate about the air screws...
The pilot circuit operates in parallel with the mains and throttle valve. Whenever the exit port in the carb throat is below atmospheric pressure, it will draw some fuel from the pilot circuit. This exit port is separate from the mains/throttle valve exit position.
The more restriction that is in the inlet tract such as air filter, ducting impedance or AIR HORN RESTRICTOR, the deeper the effects of pressure differential all along the intake tract and the more the pilot circuit will deliver at all throttle positions.
How it works.
The source of the pressure differential is the piston falling during the intake stroke while the intake valve is open. This begins a negative pressure wave that travels toward the source of the equalizing pressure (the surrounding atmosphere).
If you stopped the piston at BDTC, and all the seals were perfect, and you blocked the inlet completely. The negative pressure would equalize throughout the intake tract. (It would take some amount of time for all the molecules within the tract to spread out evenly.)
In this case, both the pilot delivery port and the throttle valve port would experience the exact same pressure differential, assuming the carbs air vents are NOT sealed.
When the engine is running, the intact tract is pulsing with air flow from inlet to intake valve, but pressures along the tract are always trying to equalize during and after each intake event. The carb ports and venturi exist within this tunnel, with each end of the tract fighting for dominance the pressure within that tract.
The intake tunnel walls and obstructions impede the equalization flow of air within the tunnel, and effect how fast the equalization process occurs, as does the size of the inlet presented to the equalization source. The inlet, in effect, becomes an orifice which then controls how fast the inlet tract can equalize with atmospheric. Smaller orifices delay equalization allowing the entire tract to remain in a deeper offset from atmospheric, as long as a negative pressure exists at the other end of the intake tract tunnel, this includes the carb's fuel delivery exit ports, both the pilot and throttle valves.
The greater the pressure differential, the more fuel delivery will occur. A restrictive air filter or an AIR HORN ahead of the filter, will increase all the differentials in the intake tract, making the pilot circuit deliver more throughout the operating range at whatever slide position, and is a major reason why the mains are restricted to #78 for the 649 carbs (which may also have some other differences to the rest of the world where 627b, 022A, 087a, and 069A carbs prevail without the air restrictor snorkel ahead of the air filter).
In summary, if you have what is pictured below on your bike, then you can expect to have more pilot circuit delivery at all throttle positions and engine speeds.