I have had my '80 1300A since new "0" miles. It has been a love/hate relationship dealing with the invisible goblins. As far as starting/idling problems go I now believe that if all electrical/ignition checks-out, the fuel-line system is simplified, and there are no air/vacuum leaks, the float levels are correct ( assuming the floats actually float), and you are still having starting/idling problems it is because the carbs are not clean. I spent many years being frustrated with these issues and have come to one conclusion ( now that I have her starting/running precisely and without fault)......the carbs were NOT clean!!!. In my opinion these carbs are not complex per-say. However if you study them closely they have a network of fuel galleries cast into them to get the idle/low-end fuel to the throttle-bore. Leaving fuel to stand for any significant time guarantees these tiny galleries will varnish and plug. "Cleaning" the carbs does not guarantee the carbs are clean. If you are 100% certain every other condition is perfect and you are continuing to have problems, then remove the carbs and clean them again. From my personal experience I had to do this no less then 6 times before I final got the "crap" removed from the idle circuits. Carb cleaner, lacquer-thinners, solvents of every type, ( I did not have access to ultra-sonic), enough compressed air to supply a planet with an atmosphere - the final solution was to BOIL them. No less then 3X for 30 minutes and with a lot of compressed air ! Unfortunately you will have no way of knowing of your success until it's all back together and it runs or it doesn't. I will also suggest that the Idle/choke adjustment will take some patience getting just right. ( I have mine adjusted so that the bike with start and idle with no choke on a warm day / add a little as required for the chillier days. Within 60 secs or less the choke can be reduced/removed.) I have a DG exhaust and I have not "re-jetted". I simply made my adjustments using the stock needle set for the best plug/exhaust color. The final reward is worth it ! Tech note: Do NOT use your wife's good "soup-pot" to boil the carbs !
NOTE: The seals on the throttle shaft ends could be damaged if soaked excessively in strong cleaners such as lacquer-thinner. The use of lacquer-thinner for manual surface cleaning and gallery flushing using a syringe is OK.