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Hm - let's see how it works cold. Vacuum advance is mainly a factor at steady level cruise. If anything there was/is a vacuum leak. That's a problem.
Stumble or hesitation is all about proper carb function and setup, although good engine vacuum plays a part. The carb needs a strong signal through it at low RPM. At idle or just off idle there is very little air moving through the carb so the idle circuit gets its signal entirely from engine manifold vacuum. Retarded ignition timing will contribute to that. Gas being heavier than air, upon acceleration it drops out of suspension for a second till things get caught up. That's the purpose of the accelerator pump circuit, to give a dose of extra fuel to compensate for that.