Honda GX340 Mystery -backfiring from exhaust and intake

Hello, I have a Honda GX340 engine that is perplexing me. It is old and very used but I can't find any issue that would lead to the backfiring from exhaust and intake.

Here are the things that I've checked or verified:
1) Cam shaft is correctly aligned with crankshaft on the factory marks, lobes on camshaft appear in good shape.
2) Spark plug appears to be sparking well
3) Valves and valve seats are cleaned and appear to open and close correctly. Exhaust valve stem has the valve turner cap in place.
4) Valves and push rods are straight and not bent. Rockers are not damaged
5) Valves are gapped to factory spec.
6) Exhaust is not obstructed.
7) I have tried to start with starter fluid and just gas.
8) I have tried to start with oil alert connected, oil alert bypassed, electronic ignition unit connected and bypassed.
9) Piston top, Cylinder and combustion chamber are clean. Piston cycles correctly in cylinder without catching.

Possible concern items (appear to be working okay, but worth mentioning):
1) aftermarket carb
2) aftermarket ignition coil

So, If anyone has experience with this type of issue or has some new things I could try, I would appreciate your help and knowledge.
Thank you in advance.

Aftermarket is not the way to go on Honda engines, use OEM Honda parts. Check air filter, do not assume anything such as spark, it either has spark or does not, be diligent, patient, & take your time, it is ok to double & triple check your work, let us know how it goes, thanks.