All LP regulators use the cooling system bypass circuit to provide coolant to the regulator. As was suggested, remove the hoses supplying coolant to the regulator and check them for blockage.
Even check the fittings where the hoses connect at the engine block and make sure they are not blocked off with gunk.
I have even had the intake get clogged with silicates on engines before and will prevent the bypass from circulating coolant so i would not leave any possibility unchecked.
Drain all the coolant from the system and check every hose and fitting, use air to blow through the hoses and engine block to make sure all path's are clear.