Backfiring issue

I have been having some issues with backfiring, and flaming through the carb.

It started a while back with a different issue, but I believe pertinent to the current issue. I have a 1967 Dodge Dart that I have owned for 8 years, and prior to this issue the engine has been pretty reliable, other than having to rewire the car from front to back. It has a 360 in it currently, although I don't know what it came out of, or how many miles the engine currently has on it.

An issue started a while back (about 8 months ago) where it was mis-firing when I accelerated hard, and would surge when holding speed on the highway. After replacing the fuel delivery system (new Edelbrock mechanical fuel pump, new fuel filter & I rebuilt the Summit 600 CFM carb that had been on the car for 8 years), that did not help. Finally took it to a shop for diagnostics, and they told me the carb was the issue. Switched to a Holley 570 Brawler carb, still didn't help. Started looking at the ignition system, and once I pulled the distributor cap, realized all the cap contacts were destroyed. Purchased the Summit electronic ignition that comes with their coil, box and resistor. At this point the car fired right up, and drove great at highway speed. It developed a new issue with a stumble off-idle as soon as I started to accelerate from a stopped position. Started looking at timing adjustments, adjusting floats and air mixture in carb, and even replaced accelerator pump. Not only has none of this helped, but has gotten worse to the point where I couldn't get it to start due to it shooting flames out of the carb. I realized the plugs were pretty soaked, so switched those last week, and amazing enough, I got it started. It would only start and run in idle. as soon as I applied any gas, it would backfire and stall. I have not run a compression check, although I do not think that the compression went to **** all of a sudden, (that may not be the right thought). I am getting ready to pull the timing chain cover to see if the chain or gears are worn and it slipped a tooth. Before I went to that level, I wanted to send it out to you guys to see if I should be looking elsewhere. Although I know I just switched the ignition system, I just have this feeling that maybe that is my culprit. I have nothing to base this thought on other than it is just a feeling.