Put a vacuum gauge on it, and check for any fluctuation at idle, and as you accelerate. If the vacuum has a rapid fluctuation at idle, you've got an intake valve adjusted too tight, or sticking, or- - -worst case- - -burned.
Do compression test, "dry" first, then with about a tablespoon of oil in the cylinder. Last thing to do is a cylinder leakdown test, where copnpressed air is introduced into the cylinder through the spark plug hole and you listen for leakage at the oil filler, the carb, and the tailpipe. Bubbles in the radiator icdicate a leaky or blown head gasket, or cracks into the water jacket. You really don't want to go there!
The vacuum gauge is also useful for timing and carb adjustment. Lean out the mixture screw(s) until vacuum drops, then back them out for the best vacuum reading. Timing is the same basic maneuver- - -retard the timing to get a drop, then advance for the best vacuum number. Good luck!
Backfiring that's not caused by mechanical problems is either lean mixture, or late timing, or both.
Jerry
