I've gone sevearal times myself, and always just checked it. The only time that was a problem was when I got to Bryce Canyon to find out the airport security had gone through my suitcase and decided to lock it after...which I hadn't done, because I had lost the key on a previous trip. Had to shoot sunset with my camera on my pack, and then later get the assistance of a garage mechanic to drill out the lock.
OK, I've been to he area several times over the years, but I don't recommend SLC as a starting point, fly to Las Vegas if you can. It will save you a long, boring drive until you get to th parks. Also check out these web sites for the Grand Circle trip.
I've been to Utah's NP's several times also, and I'd definitely agree with flying into Vegas. If you do, consider a stop at Valley of Fire on the way to Zion. I'd also recommend swinging through Bryce if you can.
I'd also consider stops at Devil's Garden (near Escalante, not the one in Arches NP) and Goblin Valley, they should both be easy stops on the way, can be quick easy stops close to parking if you need, or you can spend more time exploring.
In Canyonlands, I'd stop at False Kiva. Not sure if that's really little-known or not, but there's definitely not a sign for the common tourist to see.
I'd highly recommend "Photographing the Southwest, Vol 1. Utah," by Laurent Martres. It'll have a lot of common and little-known places to shoot, how to get there, best times of day/year etc. Fantastic resource. The Arizona volume is great too, if you're going there some day.