"had...the carbs cleaned"? You're going to catch some flack for that. It's rare to find a shop that's willing to work on an old bike. It's almost unheard of to find one that will do it well. By the time you get this fixed, you're going to find out that they didn't bother to fix your real problems, even if the carbs did need cleaned. Even if they really did clean them properly. Most everyone around here advocates doing your own wrenching. It's not as hard as your fears say it is, we'll help, it'll save you tons of money, you get to learn some things, and you may even have fun. Most importantly, you'll know it's right.
Do you also have other difficulties with idle? Very likely, you have a leaky intake system. Unfortunately, that may cost some more money to set right, but it
will be right if you inspect the whole intake system and set it right. It may cost a little, it may cost a lot. Hopefully it's just the o-rings where the carb boots meet the head (#23
here. That price looks absurd. Go
here to buy). The boots themselves (#21 and #22) need to be soft and free of cracks, as do the matching items on the airbox side. This is a once every 2 or 3 decade kind of repair. If you don't need to do the whole thing now, you will in the next few years. Make sure the airbox is properly sealed where it should be.
A leaky intake can cause the bike to run lean enough to damage the engine, but it would have to be pretty bad. You could just let it go until it becomes a bigger problem and deal with it then. But it will never idle reliably until you deal with it.
Or maybe it's some funny issue with those double-barrel carbs. I don't know much about those.