You may have discovered the reason most new motorcycles and snowmobiles now have fuel injection instead of carburators.
Does the bike only run with a lot of choke? Does it pop and snap out the exhaust? Does it die when you try to open the throttle? Early 1980's motorcycle carburators gum up really fast on today's gas and they don't tolerate six week old gas. The idle circuits have some really small holes that plug easily. If mine had gas left in the carbs (4 carbs) and it was not run every month it would have problems.
Many times fresh gas with some carb cleaner added will slowly open things up again after ideling a while and then riding a few miles until some power starts to come back. If it's really bad you may need to disassemble the carbs and clean them. They need new gasket kits every ten years or so anyway because the vacuum diaphrams above the slides get stiff.
You can reduce your problems by shutting off the gas when you are not running it. If it will sit a few weeks try letting it run with the gas shut off until the carbs are empty and the engine dies on it own (like is done with some two cylinder John Deeres). Always drain the gas tank and the carbs drains over winter. Take the battery out too or disconnect it and charge it every 4 to 6 weeks over the winter.
Are your carburators Kleins or Minkunis? Minkunis are not bad to work on, I've never had any Kleins. Figure $10 to $20 per carb kit from Dennis Kirk.com, Shade Tree, etc., more from a bike shop. $50 or more per carb to have a motorcycle shop rebuild your carbs if you remove, reinstall and resyncronize them yourself. $200 or more for a tuneup and adjust the valves on a two cylinder bike.
A Hannes or Honda service manual and a visit to a good website for your model of bike will explain it all in detail with good pictures. It's not difficult, from the other projects you have posted on YT, I think you would enjoy it.