Sorry no pictures of your obstructed pilot circuit or pop off setting, see my previous reply it's one or the other or a combination of both the carbs need to come off and be evaluated for function to determine where the problem(s) are it's a little more complicated than show and tell will remedy.
Your issue is one or a combination of two things, debris or electrolysis obstructing the circuit passageway from the pilot jet to point of exit in the throttle body or an issue with the the control arm/pop off pressure.
The single carb installation on the '97 Speedster leaves no room for error in function and it will destroy an engine in a hurry with a lean hesitation. Unlike twin carb installations with some wiggle room for error and adjustment on the pilot circuits that single carb has to be pretty much in perfect working order to meet the fuel demand of the engine before it leans out and smears the pistons from lean seizures.