Well, I got down there and it looks like:
- the factory "splash guard skid plate" sure isn't thick enough to support a jack
- it appears that some garage took the liberty of finding this out for me at some point
The plate is bent upwards right where you'd want to put a jack. I may look into upgrading to real factory skid plates. I don't take it crawling, so I don't need anything more extreme than that. (Is upgrading the skid plates a DIY job? Do they bolt in, or is there drilling required?)
I cut two sections of 2x6, 4" long each, and ran a narrow dado across the grain (across the 6" dimension). I tried using these as plates that the frame ridge can sit in, but then I noticed as I was putting the jack stand underneath that it already has a notch at the center of the cradle for this. Too bad, I used the wood plates anyway.

Next time I know I won't need them.
So, I jacked up each front corner one at a time using the crossmember near the center, and stuck the jack stand/plate under the ridge. Then I jacked up the rear by the center diff and stuck a jack directly under each suspension bracket at each rear wheel. (I will take a picture next time.) On my other car (1995 BMW M3) you're not supposed to jack the rear of the car by the diff, but I suppose the Jeep is a bit studier.
I did learn a lesson. I jacked the front up first so there was an inch of clearance under the tires. What I didn't take into account was that when I jacked the rear up, since the jack stands are a couple feet behind the front wheels, it pivots the front wheels back onto the ground. Next time I'll either jack the rear up first or leave more clearance at the front.
Once the four wheels were up in the air, air tools made quick work of tire rotation! Next time I know what to do and I won't need any silly wooden jack plates. Having a real front skid plate would have made life even easier, but it wasn't bad as it was.
Thanks for the help, Jeger! The Jeep is a lot sturdier than my old 1986 Shelby Omni GLHS. It was a challenge finding places on that unibody to jack where you wouldn't sink the jack into the soft unibody metal. Of course, that car only weighed 2300lbs.
- Chris