You could possibly have a parasitic load from the transmission, but it's unlikely. Does the machine drive OK? Does the transmission whine in neutral?
Other than that, it's beginning to sound like a problem in the pump. Either worn pump elements, worn camshaft or something wrong in the governor. Personally, I would take the governor apart to check if there's anything amiss, but that's just me. It can be done without removing the pump from the engine. How mechanically minded are you?