I had sim ilar problems. Old fuel can clog up the carbs. It sounds like the fuel feed jet above the float is not shutting off. clean the float chamber and while you are there replace the fuel feed needle and jet. Use the best fuel with less organic chemicals. If laying the bike up add a fuel additive to your last gallon or less, supplied by your local lawn mowwer shop.
In mine it even had different sizes of main jet. whether this was to aid cooler running on the rear Pot I am not sure. Please take the usual precautions, becaul fuel is a nasty fire hazzard. Som sports riders drain off fuel to a can remove tank empty it and sore it safely away with the cap open. before that run carbs dry. Just a few possible ideas for you. good luck withe the old dog