I bought a gallon of cleaner and after a good soak I reassembled it
You did the job halfway. The carb cleaner softens the deposits, but the passages must be cleared with massive volumes of air. I use very hot, almost boiling water to flush and clean everything after the soak in the carb cleaner, then I use a needle-point nozzle on an air gun to blast high-pressure air through every passageway in the carb. One carburetion instructor at the General Motors Training Center in Memphis, Tennessee used to say "Put 55 gallons of air through every hole!" That was his way of saying there's no way to overdo it when blowing passages clean. Simply soaking, then reassembling will just let the deposits harden again.
Jerry