What causes a fuel cut/backfire on a stock 22r?

I have double checked and reset my timing and ignition timing, checked for vacuum leaks, replaced plugs, wires, cap and rotor just for maintenance. I have a new ignition module and coil (HEI swapped)

New fuel pump, new fuel filter.

I readjusted my weber 32/36 carb a handful of times following the spec sheet and tuned it by ear the best I possibly could.

I am at a loss and have no idea where to go from here, any ideas?

Also, after I shut the engine off it sputters and/or restarts itself after the keys are already out. Is this an indicator of anything?

 

Backfire is usually an indicator of a timing issue, I know you said you checked that, but the harmonic balancer could be coming apart.
there are many cases where the outer ring (rubber sandwich with the inner) has moved in relation to the actual crankshaft position.
maybe check to make sure the cylinder is at TDC with a straw inserted into the #1 cylinder as you slowly hand crank it to the top of it's stroke and see if your timing mark lines up with zero.