another intermittent starting problem

[old Rusty C10]

truck is a 79K10 350 v8 with automatic
took the truck to get inspected the other day and it massively overheated. Towed it back home and put water in radiator. I was able to get it started and was using it around here . It would shut off it would crank but wouldn't start.
The first time it happened I decided to check the gas as the gauge doesn't work . I threw gas in after a half hour going to get gas and it started ran for a little while. I was using the truck to push things around It did stall a couple of times but started right up.
It cut out again again cranked like a SOB wouldn't start. this time black smoke was puffing out the tail pipe and using a screwdriver it did not have spark
I checked the cap and rotor and the rotor had a large black burn mark on it so I changed that out with a cap with coil and rotor I had and it started it and worked for another short bit when it cut out again . I immediately checked for spark and no spark but black puffs out the exhaust so I changed out the module in the distributor. It still wouldn't start so I hooked a chain around the truck and with my son I pulled the truck about 30 ft . He tried the key after moving it forward and it fired up . I parked it and I haven't touched it since
I should also mention we put a brand new exhaust on the truck ( walker pipes with a rock auto cat and standard muffler) and we threw a new 1406 edelbrock carb on it a week ago as the OEM carb was kinda cruddy.

I am kinda stumped here the carb does not push black smoke upon start or while running just when it stalls and it only cranks.. Im wondering if the whole distributor needs to be replaced? ideas?