My money is ultimately with Dave’s solution; but it is ALWAYS good to start with a compression and spark test, pretty much every time, so you don’t go off half-cocked, down some worm hole. You don’t want to waste time or money if the compression is bad. Also, with Big Twins and others, it perfectly possible that spark on one cylinder might be dropping out at low speed. Check compression first, spark second and then go after the carb. When checking the spark, make sure in your case, that the mag plate is in the idle position, because sometimes, wires chafe and will only short out in one place in the throttle travel.
Long live American manufacturing!