I have been using the big chief smoker for years and i do not think a propane burner would work.
I think it would be to hot. However i don't use the insulated blanket i just wrap an old coat around the unit and set a temp control unit at top 170 and it should and will take a long time to bring the meat up to the 153 i am looking for.
During the colder months like now. I smoke out side most of the day and try to pick a sunny day so i can have the unit in the sun then using the temp control that i added to it i bring the temp up in stages. 150 for a couple hrs with smoke 160 couple hrs with smoke and then 170 with the coat on it and then i will bring it in to the house and just use the heat only to finish off.
You can also just do a water bath for the sausage. Just bring the water up to 170 and slowly cook the meat until it reaches you target temp.
Most sausage is done that way i think and it does not make the meat less smoky. Works great.
My favorite is to use the Big chief for the whole thing though. For that i need to bring in to the house.
Smells better then potpourri.
Realy though it smells no different then just bringing the smoked meat in to the house to put away.
Happy Smoken