It very well could be gummed up carbs, specifically clogged pilot jets. Especially with that wonderful ethanol crap in our gas now. As a service writer in a bike shop, $350 sounds about right to get the carbs out, take 'em apart, put 'em back together and reassemble the bike. It is time consuming and of course there's the cost of cleaners, rags, etc.
The problem with just spraying carb cleaner through the carb is that you need to get it into the pilot circuit. You really have to remove and strip the carbs to do it right. If the pilot circuit is blocked now, cleaner isn't going to get in there to flush it out. You will have to force cleaner into the pilot circuit and/or use compressed air to blow through the circuit.
Having said that, If you're lucky, just the pilot jets are clogged and you can remove them from the carbs without removing the carbs from the bike. Once they're cleared, maybe dose a tank of gas with some seafoam or techron to clean any accumulation out of the jets.
Have you worked on your carbs before?
I would try this, which you should be able to do on the bike; Drain the carbs. Remove the float bowls. Use a small screwdriver to remove the pilot jets. Blast them clean with carb cleaner. Put it all back together and see if it works better.
This thread shows how to get into the carbs.
I don't think it talks about the pilot jets but they are next to the main jets recessed up in the carb body. Maybe one of the other carb threads in the stickies has some specific info on getting to the pilot jets.