I have a craftsman tractor with a B&S 18hp engine
(31h777). The engine will start and run but backfires at pretty much any speed under 3/4 throttle. I changed the spark
plug (old one looked good and was gapped correctly), adjusted the valves to .0035 on intake and .006 on exhaust (they didn't appear much if any out of adjustment before starting). Rebuilt the carb (didn't seem bad). Nothing has solved it. It seems to be backfiring through the carb as there is a puff of white smoke from the air filter when it does it. What is the next thing to check?

Thanks.