Believe it or not, I think I may have fixed this crazy Pal.
After I got home Friday I put back the original HDD (in its original bracket) so that I could send it back Saturday. Then I decided I needed to make sure it was still rebooting itself like it had been, so I hooked it up one last time.
And it ran all evening without rebooting. Even woke up and recorded a cartoon Saturday morning.
Unfortunately it still wasn't quite right, because it rebooted again Saturday evening. But that was still a big enough improvement, I decided there was hope for this thing after all.
So I put my HDD back in. This time it rebooted after about an hour and 15 minutes.
I really didn't think there was a problem with my HDD. I hadn't had any trouble with it at all in my old Pal, and the new Pal had first rebooted with its original HDD. But maybe something happened to the SATA cable or connector during shipping?
So I took it apart once more, pulled the main board, and gave the SATA connector a close visual inspection. I saw what appeared to be a metal filing at the base of the connector where it's soldered to the board. I wasn't sure though: even with a good flashlight this is really hard to see because it's soldered to the top of the board and there's only a millimeter or so between the board and the connector housing.
I also thought I saw some metal filings within the connector housing itself, where the cable slides in. So I got a sewing needle and very carefully used it to remove any visible debris.
Then I put it back together and so far, it seems to be working. I'll give it a couple more days to be sure, but I'm very cautiously optimistic.