Points that are barely opening can also cause poor running and backfires. They "bounce" and/or break the circuit at the wrong time.
Did any of the tests you performed from the #7 post result in any fixes? If so, which and what was fixed?
Have you ever removed the distributor or loosened the clamp at its base?
Are you sure the plug wires were put in the new cap in exactly the same position as they came out?
If it is backfiring you have spark but either you moved the distributor or swapped the plug wires. Get it to Top Dead Center and see if the rotor is pointing towards the line marked on the edge of the distributor with cap removed and go from there. Rev limiting rotor and no limiting should have the same configuration, they don’t point differently.
All of the tests suggested above provided the correct results indicating that nothing was faulty. I believe what was happening was that the points were in fact grounding due to the square style grommet.
There is a mark on flywheel and front of crank on the harmonic balancer but easiest way is to remove valve cover and see if line on pulley lines up with oil sprayer bar. The crank turns twice for one revolution of the cam but just make sure cam lobes are pointing down at 5:00 and 7:00 on piston #1. Firing order is on the valve cover, trace each plug wire to the cap to make sure in the correct order.
Both rotors are pointing in exactly the same direction.
Removing valve cover is the easiest route, gasket will be fine. The timing mark on the cam pulley will be right under the spray bar. Find the mark in the dizzy and turn it until they line up then tighten dizzy. The engine sits at an angle, pretend it sits upright, cam lobes will be at 5 and 7.
yes sounds like your plug wires are not in order or your timing somehow got way off, is your distributor loose?
you'll have to put your engine at TDC. Pull the plugs and rotate your enigne until the timing mark on the harmonic balancer lines up with the notch on the timing chain cover, the "TO" ball is visible in the timing light window on the flywheel, and the rotor points to #1 cylinder (there is usually a notch on the distributor too). This is important because it can be 180 degrees off if the rotor is pointed at #6. Once these are lined up turn the distributor counter clockwise a little and tighten down and it should start. then set the timing by the book.