Out driving. Shut off car. Dead. What is this?

[SS4Real]

I also had the same problem as you described on 2 original LS-5 454's. If the car starts with no problem in about an hour, you may have the infamous heat-soak starter problem common to older or worn starters. As quoted in many technical articles on this subject, for some reason Chevrolet engineers located the starter and solenoid right next to the exhaust manifolds. Ford did a better job and moved it away from the heat robbing culprit. I tried thicker cables, heat shields, etc but did not have very good luck. I ended up simply putting in a new starter and solenoid combo and it fixed my problem. In addition, if you're running high compression, that seems to amplify the problem even more.