I realize I never responded to this post but did end up finding the problem.

The main 12V wire that goes from the alternator underneath the crank pulley and connects to the starter had an intermittent connection right under the crank pulley where the wire harness is essentially clipped to the block.

The harness in this location had grown very stiff with age, and resistance measurements across this run of wire varied wildly when the car was hot and the engine was running (vibrating).

I'm not sure if it was corrosion, fatigue, or a combination of both that did it, but there was a heat and vibration dependent partial break which resulted in large resistance swings. This wreaked havoc on all the 12V systems when the car was hot.

Replacement of this run of 12V wire completely eliminated the issues.