Dave, thanks for the input.
I asked my wife to repeat the number to me, and she repeated 0.8V. I didn't check it when I got home (I don't remember) but I should have verified. I don't know how a battery can read that low and come back.
The 4.7L starter does have contacts that can be replaced if intermittent starting is a problem, but this is like my whole electrical system shuts off, so I think it's different. Maybe someone who's experienced starter contact failure on a 4.7L can chime in if it's similar.
Brian, I used some battery terminal grease in the little packet from the auto parts store, and I believe I put it on after I put the terminals on the posts. There was not a lot of corrosion, but enough that I decided to repaint my hold down bracket and pull the battery out and spray some paint under my plastic battery tray.
There are two aftermarket electrical items that I'm aware of in this vehicle: an aftermarket rear view mirror with compass and temperature indication, and an ASC sunroof installed by John's Sunroofs at Belleview and Santa Fe. Neither have ever seemed to cause any problems previously.