If the compression test comes back within tolerance when warm, then we may need to revisit the firing order. The way I'm reading the steps taken to this point is that the backfire happened after the tune up? You had previous running issues that were fuel related before, but now that the carb is correct, the ignition is suspect.

We won't pick fun at swapping or leaving out parts. It happens to the best of us. A very competent rifle builder bought everything to build himself an AR several years back. He worked and polished everything to the way he likes his weapons to run. He took it out to the test bench behind his house and loaded a mag half full. He touched the trigger, and the rifle unloaded the mag on full auto. Long story short, don't forget the sear spring. He found that he had forgotten it on the bench.