have you checked the exhaust and manifold for leakage anywhere? look for any holes in the piping, if it pulls in cold air back into the engine it will make it backfire.
Also check the intake as well, check around the carb/mixer for any open ports, check lines for cracks etc.
you can usually use penetrating oil and spray it in places you suspect and if it changes the way the engine runs you found your leak.

This is just a suggestion since you seem to have eliminated everything else. It just sounds to me like you have an air leak somewhere.