Welcome aboard, Cove.
We do need more info about the motor. Having the serial number helps a lot.
When this happens, the throttle is wide open and the motor cycles from WOT to idle until you chop the throttle. What happens at other throttle settings? Say running at mid-throttle or 3/4's, does the motor eventually fall over to idle?
I would eliminate the external fuel system by using a portable tank with it's hose. If it runs OK, you know it's the motor.