It's been a long day but I am on the road to whipping this thing. I started the day off by replacing #1 and 3 plugs again. The temperature on these two cylinders immediately came up but the random backfiring continued. I checked the reluctor gap again and it was OK at 0.008". I took my Eddy carb off of my Duster and put it on. No change in the way it ran, still backfiring. Tried another ECU...still backfiring. Tried yet another distributor cap...still backfiring.
When the owner brought me the car he told me there had been about 4 or 5 gallons of gas in it for 5 or 6 years so he put 10 gallons of new gas in it to dilute the old gas. I thought this might be the problem so I dropped the tank and dumped all of the gas. Blew out the gas lines and emptied the bowls in the carb. Put 5 gallons of new gas in it and fired it up. Still backfiring.....damn.
I dug out the old spark plugs that were in the engine when I got it. Took them over to the bead blaster and cleaned them up. Put these old plugs in it and the backfiring went away....SUCCESS. The engine is running really good now. Still having a little trouble getting the idle down to where it should be but that is small stuff compared to the constant backfiring. I'm sure it has a vacuum leak somewhere so I'll be finding that tomorrow. The car doesn't have power brakes so that's not the issue. I'll find it. I finally had a successful day. Thanks everyone for you ideas.
By the way, the new plugs that were causing the backfiring were Champion RJ12YC. The old plugs that are working are Autolite 85.