Losing my mind trying to get this 360 to run right

I think a lot of your frustration is coming from running open exhaust and a rich mixture. If it's scavenging cold air from the lack of exhaust, it can cause the popping, you're talking about.

I wouldn't blame the distributor, just yet. Have you checked total timing?

The second you put pipes on that thing, it's going to need tuned again, anyway, so that's the first thing I'd be checking. Depending on the overlap of your cam and vacuum needs of the engine, it may not idle well without tubes.

I know when I fired up a Toyota 22R that I was putting a glass pack on, it would not idle at all on the factory timing, with a short exhaust system.

Those double pumpers are also sensitive to float flooding. The screws on the float bowls that adjust fuel level usually need tinkering with them.

That could also explain the rich condition/ popping with short exhaust. The carb may be flooding from high float level. You could try that, before exhaust to get it to idle.