Well the number one rule in my books when an A (or T) is backfiring is that there is a vacuum leak at the carb or intake gaskets.
Another problem area is the pigtail wire under the distributor plate.
If the wire is frayed it can intermittently touch the distrib body and ground out.
As the vehicles dies/stops pulling, the ground releases and the vehicle pulls forward again and the wire again touches.
...As the engine warms up, any slight greasy film turns to liquid and if there is a slight greasy sheen inside the distrib body (as there was in mine), the grease turns to liquid and is then able to pass the current of things like frayed wires to the ground of the distrib body.
Having said that, The resulting jerky thrust of the confused engine doesn't necessarily cause a backfire but rather just a rapid on/off 'lurching' movement.
...I would tend to believe your problem may be in the carb/intake and delivery of air/fuel.
Again, as the engine warms the intake manifold warms and expands at a slower rate than the quick to rise engine.
If an intake/carb gasket were on it's last legs this is the exact time that it would become noticeable -shortly after engine start- in that the engine is hot and has fully expanded and the intake/carb is still rather cool.
At that time the greater thermal expansion of the block may be just enough to cause the smallest of crease or tear/imperfection in the gasket (or machined surface) to allow air to be sucked in thus throwing your carbs precisely metered air/fuel ratio out the door.
jmho, I would suspect the intake and or carb gaskets or possible loose/cracked manifold or bolts..
moe