Testing my memory.
A long time ago, Dad had a more modern (454) engine that would very occasionally let loose with a backfire that sounded like a cannon.
Culprit turned out to be a graphite gap in a factory radio suppression spark plug wire. Guess how long it took to find that!
If the load was just right and the ignition advance was at a certain point, KA-POW!
Not saying this is your problem, but my vote, like others in this thread, is ignition.
Will be interested to learn the solution.
Jon