I visit Moab frequently with my Jeep so if you have any Moab specific questions I might be able to help.
As for your drive to Moab, I would recommend checking out the Grand Canyon of Texas (Palo Duro Canyon State Park). I never tried it, but from the highway I remember seeing a bunch of rigs driving out in the semi-dry river beds near Amarillo. That would be fun. Also in Amarillo, if you can eat a 72oz steak by yourself in less than an hour it's free!
In New Mexico you can Jump on Historic Route 66 for part of the drive. I hear some abandoned parts of it can get a little rough and fun to drive. I haven't done that section, but the Historic part through AZ had some quirky nostalgic shops and restaurants.
It would add some time, but rather than heading North at Shiprock, NM, I'd include Monument Valley if you haven't seen it. There's a short easy dirt/4x4 loop through the Valley where you can drive through the monuments. Four Corners Monument is in that area as well as Mesa Verde National Park, but I like Monument Valley and the drive through Mexican Hat the most (by far).
Upon entering Moab, instead of taking 191 up you could exit near Montcello towards the Needles District of Canyonlands. From there you can 4x4 all the way up to Moab from the Hamburger Rock Campground, through Lockheart Basin, over Hurrah Pass, and down into Moab.