318 backfired and now runs like it has a misfire

I would pull all the plugs and run a compression ck as a first step. Any cylinder that is way off (15%) would be first place to look for bad push rod, collapsed lifter, broken spring, etc. If nothing shows up, then you can chase ignition issues. I would not install the new dist until you have done this.

Perfect answer^^^^^^ This is where to start.