1965 383 Plymouth Backfiring..any Help

My 65 Sport Fury still has the original 383 Comando V8 factory 2 bbl motor in it. It spun a rod bearing in 1973 and I still have the 1973 Arizona license plates that came on it. I rebuilt the engine. That was the easy part. The hard part is finding the backfiring problem. As you accelerate about halfway or better to the max rpm, is when it starts to backfire. The first thing I think I should do is to measure the slack in the timing chain. Any other idieas? I rebuilt the engine in 1995 and now can’t remember if I put new timing chain and gears in it. I am sure I would not skimp on such an important item. I think I had my father looking over my shoulder back then and he talked me out of spending money on chain and gears. I have done the research for troubleshooting the timing chain wear. The slack in the chain is not suppose to be any more than 11/64 of an inch of play. I can’t beleive that I would not put on a new set of chain and gears. Could it be the valve springs? The valve springs and valve guide seals were new when I put in the new camshaft. I put in a slightly higher performance camshaft then what is stock. With that camshaft kit came new hydraulic lifters and the new valve springs. I assume the valve springs would be a stiffer spring than stock. The point gap is set right at 18 with a new set of points. It can be anywhere between 14-19. The timing is right a 10 degrees BTC. That is what my 65 Plymouth service manual said to set the points and the timing at. I called the place where I got my camshaft and asked them if the factory timing can still be used with the camshaft they sold me. They said “yes”. I no longer wanted to use the high rise aluminum intake and 4 bbl set up so I installed a new valley pan intake gasket and put the original factory cast iron intake back on it. I put on a rebuilt Bendix/Stromberg WW3 2 bbl carb. That is the factory correct carb for my car when it was new. I still have the original but this one was already rebuilt and ready to go. I am getting very good spark from the wires at the distributor cap. The spark snaps and jumps very strong when I take them off one by one at the cap. When I do that I don’t really hear any difference in the engine. It isn’t obvious that a wire has been taken off if you just listen to it run. It basically makes no change. That’s the way it seems anyway. I guess I need to do the same thing at the spark plug end of the wires to see if I am getting the same good spark. Maybe I should check the plug wires to see if I have two of them switched around by accident? I wonder if my distributor drive gear might be off by one tooth? The distributor itself can only fit into the slot at the top of that drive gear one way. It is either dead on or gonna be 180 degrees off. It could be that I am off by one tooth of where that drive gear is supposed to be, in its relationship with the camshaft. That could put the distibutor off just enough to be a problem. Does that sound possible? Maybe the timing marks on the camshaft and crankshaft gears are just off a tooth. What do you guys think? Please help.
I bought the car in 1987 and finally rebuilt the engine in 1994 and then drove it for a year and then parked it in my garage in 1995. I looked at all my receipts and I put in a rebuilt distributor at the time I put in a new camshaft. The engine has a total of 3200 miles on it. Can’t imagine the distributor and/or a cam lobe going bad in that short amount of time. Glad you guys are willing to help. It is blowing a little black smoke out the exhaust as if it had a manual choke that was pulled out too far and forgot to push it back in after warm up. It has a well type, thermocoil choke spring set up sunk down into the intake manifold. It is supposed to be set at 1 notch rich. I’ll check that to see if it needs adjusting. Any other tips? You guys are good to help a person out.