I would still suspect the carbs or even the CDI unit if this is a CDI bike.Put your bike in with your info.You may think you have cleaned the carbs but many people overlook the slow speed circuit under what I call the,"Black Banana" in the top of the carbs.All these holes should be soaked with some kind of CLR(Calcium Lime Remover) or left to soak in white Vinegar(Never use vinegar on accelerator pumps or Vacuum pet cocks if fitted.They are made of different metal and will dissolve)
Then all holes really well blown with high pressure air.Also is the black rubber bung present in the bottom of the carbs in-between the jets?
Also a lot of shops don't want to touch these bikes and will charge you an arm and a leg.
Lets go back a bit.Are you getting a good spark on that side.Don;t put the plug on the cylinder cover as that's insulated from the frame.Use a better part of the engine or a bit of wire around the outside of the plug to a good ground.
Also depending where you live join Chopper Charle's site,
http://choppercharles.com/cs/forums/as well.There may be some one close you you who can help.