Heavy backfiring at llow speeds

I donít know if this should go under Cars & Minivan or Trucks so Iíll put it under both, as this is a small motor home.
I have family in New Orleans so was anxious to get there after Katrina
and took off knowing that I had a deal hole on# 6 (burned valve). Iím driving a 1977 Concord motor home with a dodge 360-3 engine. I put in new plugs and a new carburetor before leaving.
It didnít have all the power I would have liked but it ran OK and I made it there. I headed home (Tigard Oregon) after a couple of months and got as far as Phoenix Arizona. I donít remember if there was a pop or loud noise of any sort but suddenly I could barely make 20 mph. I got towed into Phoenix where I was told that #1 and 3 cylinders were bypassing gas (raw gas squirting out of carb). He pulled the heads and we swapped for a rebuilt set. He seemed to do a good job and the engine ran fine. After leaving Phoenix I was able to make hills at 60 that would have been 45 before the heads were replaced.
I made about 800 miles and then everything went to hell. I could barely get it started and when I did, it sounded like it was a shooting gallery. It was backfiring worse than Iíve ever seen. This started about 20 miles from a city and I pushed on only to find that once I got above 45 or 50 mph it seemed to settle down and ran well enough that I decide to carry on because I really wanted to get home.
I finally made it and was glad to walk away from it. But now I need to get it fixed because I want to go back and work with Habitat for Humanity to help some of those people who have lost so much. But I donít have a clue of where to start. I am thinking about shot gunning in a new distributor to see if that helps, but that is only a guess. I would really appreciate some guidance.
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