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Be sure your "starter valve" (part number 27583-88, #48 in linked exploded view below) is fully seating. There is no "choke" on those carbs. A choke is a butterfly mounted in the front of the venturi. Those went away with the switch to CV carbs.
Chokes don't leak but enrichers can, and if they are pulled slightly off the seat can mimic flooding. The black viton sealing area on the starter valve can wear too. I inspect those using a bright light. As mentioned above vacuum fuel valves can malfunction. If their diaphragm pinholes it can pass fuel straight to the engine. (That's one reason I get rid of them on my personal bikes.)
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Slideshow: The bar-and-shield logo shows up on far more than motorcycles, some of the company's most unexpected products have nothing to do with riding.
Slideshow: From the troubled AMF years to modern misfires, these bikes earned reputations for reliability issues, questionable engineering, or disappointing performance.
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Slideshow: The Swiss custom shop has taken a Harley Softail and stretched it into something so long and low that it looks closer to a rolling sculpture than a conventional motorcycle.
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Slideshow: A standard cruiser becomes an intricate metal canvas in the hands of a Swiss custom house known for pushing Harley-Davidson platforms far beyond their factory brief.
Slideshow: Harley-Davidson's challenges aren't abstract; they show up in dropping shipments, shrinking dealer traffic, and strategic decisions that aren't yet translating into growth.