FWIW:
After new plugs, new coil, new coil wire, rebuilt ignition system, rebuilt carburetor, "everything" mentioned checks out "OK" and it starts right up .... but, "backfire".
Running "again" is mentioned ..... however ...... One Question: But, how long did it sit "NOT" running?
One Possibility:
Sometimes while sitting idle for a spell, oil and fuel can evaporate from Model A valve guides and valve stems and leave a sticky residue of sticky varnish ..... thus causing slightly sticky valves causing slightly rough running and backfire.
If so, "valve timing" is not properly coordinated and the atomized fuel mixture can arrive and exhaust later from in the combustion chamber where the spark plug ignites the fuel when the exhaust valve is in the open position.
Somewhat similar to an "open" exhaust valve is ....... you can hear a firecracker explode in a bathroom much better when the explosion sound travels through an open door in a bathroom ........ no end to what one can possibly find with 80 year old people.
One cup of Kerosene poured in each spark plug hole and allowed to sit for 24 hours was the vintage cure .... some today use transmission fluid, Marvel Mystery Oil, etc., to dissolve the stick varnish.