Got an old 1964 Chevelle with a newer 350 crate engine, and having some issues re-starting it after its been running for any amount of time.

It will start no problem on the first crank, runs just fine to wherever you want to take it and park it, but if it gets turned off, it won't turn over again for 20-30 minutes. Once I've waited the requisite 20-30 minutes, it'll turn over and start again no problem.

So far, I have replaced the starter/solenoid, battery, and in-dash ignition switch.

To reiterate:
It cranks, turns over, and starts without issue on the first try
It won't even turn over again (no crank) if its been turned off after any amount of idling/driving
Waiting 20-30 minutes seems to miraculously cure the condition

Although I enjoy tinkering, I'm not a mechanic and have replaced what I think are the "usual suspects". Any ideas out there?

 

2 things.

1. Is it a mini-starter or a normal sized "big-bodied" starter?
2. Have tried chaging the control module. That's if it's got an HEI dist. in it of course.