Off idle hesitation - solved

I basically agree RRR.
But on a very very gentle acceleration the pump shouldn't do much and the problem should be noticibly less.
I'd be curious how it acted in neutral. I think what I'd do is check the spark plugs and in the cap (because they alsways have potential to reveal a good clue). Then take the aircleaner off and observe the carb and engine while manually opening the throttle. If it happens under no load, then it will certainly happen under load.

@hotrod swinger
With two idle circuits, each one contributes the same a single would have. That's a long way of saying 1/2 turn richer on each mix screw is probably double what it needs.
I have taken the air cleaner off and manually operated the throttle to observe the pump shot in operation. Sometimes there is a hesitation, most times not.