Good to have a cap and rotor with brass contacts; they last much longer than the factory style aluminum ones. That's one of the things my Dad taught me, and it's proven right many a time. My Burb is a vortec 350, but they eat cheap rotors too. Until I got a Blue Streak one, and it's been in the truck for 2 years of daily driving in Houston, Texas traffic. The cheaper white rotors would only go 6 months at the most.
I agree with the guys that it must be the pickup coil or something else in the distributor. Because it definitely sounds like heat soak from your description. I've had modules do that too when they're going bad. From your username I presume you have knowledge of the early style GM HEI distributors, with the huge cap? The reason they got away from those is because in hot or humid weather, if the vehicle was run hard and the rotor went bad, the coil would cook the module. If I had a dollar for every early HEI rotor I've seen with a hole in it, I could buy another truck LOL. The factory style rotor plastic couldn't tolerate 40,000 volts indefinitely, so they'd get a pinhole burned in the recess under the terminal that the cap carbon button contacts. Blue Streak came out with a rotor in the mid 80s to help with this. Had one in every car and truck we ever had, lasted a lot longer. The dielectric compound is a must use on any HEI module, even the ones not in the distributor like the vortec engine.
It's also entirely possible that you have a bad module. "NEW" doesn't mean "GOOD".
Hopefully all the advice you've gotten helps, and you can get your truck reliable again. Last year I was ready to shoot the Burb because of a similar problem. I figured out what it was by process of elimination ( like you're doing), thanks to good advice on this forum. Good luck and let us know how it goes.