The impuse engine is a neat idea. I don't know if it's possible to get the expansion to also flush the combustion chamber without an additional large area valve somewhere on your chamber.
The nozzle acts as a check valve only allowing gas flow forward. You'd need a low cracking pressure large area valve on either the left or right end of the chamber. You can probably get away with a thin shim of steel flapped over some 3/16" ports. The explosion would push the shim pretty shut, but when the nozzle valve checks shut the steel flaps would open up and let fresh air in.
Unfortunately you'd have to wait for the chamber to cool down and the gases to contract to draw in fresh air and a measured injection of propane. Without an open airflow, either the straight through or the U shaped jet path, I don't think you can get quick enough recharge of fresh air.
Want nearly free GBB gas?