And the weirdness continues...
I went out there again to test the voltage at the engine bay fuse box and it was reading 12+ volts. So I went back to the kick panel and stuck the voltmeter probe in there and I got 12+ volts. Then I went to the cigarette lighters and tested and got 12+ volts.
So I'm thinking one of two things is happening here... either there is a loose wire going into the back of the kick panel fuse box OR there is a fuse/wire that is failing once it heats up.