Removing the tank is about the easiest thing you can do on this bike, so don't let it worry you if you have to do it. Have you cleaned the carbs since buying? I'm no expert, but it could be a stuck float valve? Were you idling normally before this issue, or has it idled this high since purchasing the bike? When I bought mine, it idled really high, but I think the previous owner turned the idle screw way up to keep it from stalling at lights (it needed some work). So perhaps that is due to the idle screw.
I'd clean the carbs and give the bike a test after that. If it solves the dying problem but still idles high, try the idle screw