More carburetor questions and opinions..

I imagine the first stage works like metering rods; suppling fuel under light to moderate acceleration.
What kind of manifold vacuum numbers is your combo posting?
Does it hesitate in neutral, at tip-in?
Does it hesitate immediately, right off idle?

A think the biggest clue is the mixture screw behavior. If they are in fact reverse operating, then it sounds like all the way in is richest, which leads me to think that they may be air screws. In which case the engine is craving more idle fuel, which is manifesting as a hesitation.I would then conclude that the carb is failing to deliver enough idle fuel.In which case I would take it apart,figure out that circuit, and mod it as might be required.I suppose theres a real good chance that the missing fuel is supposed to be coming from the 2-stage.In which case that two stage could be functioning in an anti-diesel capacity;shutting off the fuel when the vacuum collapses at engine shut-down, and allowing idle fuel at start-up, with rising vacuum.
This is all speculation. Ive never had one apart.