My guess would be the excess ammonia and organic sulfur (sulfur dioxide gas is rather poisonous and used as an industrial cleaner) left from years of waste. And for gods sake, don't hose it with bleach! Bleach + ammonia = chloramine vapor! Chances are there's some fun molds playing around in the wood there too, some of which will cause reactions with just a few minutes of exposure. I'd say it's not the propane but what the heat is doing to the atmosphere within the coop. A slight temperature change will change the fluidity of gasses drastically and stir up whatever is causing your reaction. Pour a concrete floor, treat and seal the walls properly, insulate, drywall, add an extractor fan or two, run some plumbing, 100amp electricity, perhaps a wifi extender and enjoy a really nice shop once it's taken care of.
J