All I know is that the dealers were told to only use DEX/MERC III in an AW-4 until after the 7/70 warranty ran out on the Jeep Cherokee. That says something to me.
Since no fuses sound like they've been tripped, I'm kind of leaning towards the alternator idea too.
I had an alternator problem with a previous (non-Jeep) vehicle and it had the similar sort of voltage swings that you describe. A new alternator solved the problem.