I'd drain the carbs while on the bike (try to catch what comes out with a piece of hose and a container looking for rust, water, trash, etc). Once drained, put Seafoam in as mentioned above and let it sit at least over night. If its ridable after that, I'd put some Chevron "tectron" in the tank as well. It works very well at cleaning out the entire system...
If that doesn't work, remove the entire carb rack WITHOUT unbolting -(KEEP THE 4 CARBS TOGETHER AS A UNIT), it should come out all 4 carbs. Remove the float bowls and clean out the jets using carb cleaner and an air compressor. As long as you don't adjust the sync screws it shouldn't make the sync any worse/better. Once running correctly, you can do a sync. As stated above, the sync helps more with rough running/ vibrations.
I suspect the carbs will be very gummed up...
If that doesn't work, remove the entire carb rack WITHOUT unbolting -(KEEP THE 4 CARBS TOGETHER AS A UNIT), it should come out all 4 carbs. Remove the float bowls and clean out the jets using carb cleaner and an air compressor. As long as you don't adjust the sync screws it shouldn't make the sync any worse/better. Once running correctly, you can do a sync. As stated above, the sync helps more with rough running/ vibrations.
I suspect the carbs will be very gummed up...