Unusual Backfiring Problems

Hey guys first off thanks for all the advice.
The timing was checked with the vacuum off.
We also checked for a vacuum leak and it was all good.
I have TTI headers and I checked for a leak and there was none.
We have tried adjusting the carb numerous times and before the electrical problem it didnt back fire.
We are going to try replacing the ignition box. Is there anyway to test it?
When we had the electrial problems we replaced the pick up coil and gapped it correctly.
Also double check the spark plugs and wires they are all good.

I will keep you updated about the ignition box. Also open to more suggestions

Thanks again

i still recommend changing the distributor cap ($5 bucks) before pulling the valve covers and all that. really. had a very similar issue and that's all it was. drove me nuts until i figured it out. the cap had a hairline crack in it.