Fuel, spark, no starting and fouled plugs. '68 Mustang 302

Hey guys was hoping to get some help on an issue I'm having. And this forum has done wonders for me in the past. Hopefully I get that lucky again.

I have a'68 Mustang with a rebuilt bored '73 302. I only get to go work on it a couple of days a week. I had just finished putting all brand new suspension on it, and was finally ready to fire it up. I had to tinker with it for a little bit because it had sat, but eventually I gave it one pump of the pedal and BOOM it fired right up. I let it run for about 5 minutes, bolted down the distributor and shut it off because I was going to put some flush in my radiator. Got right back in the car and nothing.

It will crank and crank without hesitation. And it almost catches and then nothing. It has sputtered through the carb a few times. It's backfired a couple of times. The timing is set 110%. The wires were new (they were Accel's but I noticed the further back my cylinders go, the weaker the spark) so I put my old ones back on.

I set my points 18, and it sounds like it wants to catch, I set them at 20 and nothing at all. I even drained all the gas I had in it (it had stabilizer in it so it should have been good) and put new in. The carb was professionally rebuilt too. The only thing I hadn't tried was the plugs, and they were covered in carbon. So I cleaned them up and put them back in. And by just cranking it a few more times, they were covered again, but they still seemed like they were getting plenty of sparking holding it next to the block even with the build up. I even put a jumper wire from the battery directly to the coil. I've even taken my valve cover off to make sure my new cam was working, and took the gas cap off in case it was vapor locking. I have Iridium plugs in it, I'm going to put some new copper ones back in it probably Sunday. Seems like the copper ones are always better than the pricey ones anyways.

I'm just lost as to what this could be. Especially for how quick it fired up the other night, ran perfect, and within 3 minutes it does nothing at all. Everything in this motor from the fuel pump, to the timing chain, to the cap and rotor, to the carb has only about 200 miles on it if that. I even have 2 brand new coils (one is suppose to be a spare for in the trunk) that I flip flopped just to try that. Since it did whatever it did, I do kind of have to feather the gas pedal to get it to almost catch. But I did the old fuel line in a pop bottle trick and the pump is working perfectly, and the gas is clean as can be. So I'm completely lost. So anyone with ANY kind of a suggestion please give me your 2 cents. Thanks as always guys! Drive safe and Happy 4th!

I also have a Pertonix ignitor I'm wanting to put in it once I get this squared away, and for the price, it's just getting some shelf time.