Your statement about "frost on the propane stuff" makes me think that the J-model fuel regulator (what the coolant hoses run to) is leaking liquid propane into the intake. What you think is acting like it's out of fuel is in reality probably "over-fueling". I have always found that a simple way to test this is to shut off the supply valve on the propane cylinder and see if the engine begins to run better as the fuel in the hose is consumed.
If the condition is due to over fueling, the engine may seem to run "about right" just before it uses up all the fuel in the hose and dies.