Part of the problem is a full tank. Won't your petcock valve shut off?
The real problem is your float needle valve. It si like the flapper valve in a toilet tank that won't close properly.
If you have any lawn mower shops near you, go see if they can sell you a plastic 3/16" inline shut off valve. You can put this on the fuel line AFTER the tank fuel petcock valve and BEFORE the carb. This will stop the flow of gas when the moped is sitting, not running but won't solve the problem of the defective float needle valve when the fuel petcock valves are open and the moped is running.