Thanks all for the kind words.
Nico, it was pretty much all off trail. On the west side of the park I walked about a mile of 4x4 road and I walked a mile or so of trail in the Klondike Bluffs area. The larger scale navigation is pretty easy. The 10 meters in front of you is the hard part; lots of big cracks, avoiding soil crusts, and finding your way around/over slickrock domes can be tricky.
Jeffery, a short answer (maybe I should put together a bit more later...): you're right that a canyon country skill set is pretty different from the Sierras or PNW. Honestly I don't think a GPS would be much help, at least when it comes to getting in or out of canyons (unless, for example, you know ahead of time where the entrance is and you're using it to get to that point), If you have the time, there's not much risk in walking up canyons. I recommend it. Finding ways out can be tricky, and ways in even trickier (it's usually much easier to see a route out from the bottom than a route in from the rim). At least a little bit of familiarity with the geology of the canyon is helpful (some layers are more likely to have breaks/routes out). Game trails are often helpful. Vegetation is helpful. Really the best thing to do is do some established routes and pay attention to the trails in and out of canyons. In most places, the same entry/exits have been used by people and animals for hundreds or thousands of years. Sometimes it requires lots of walking back and forth on benches to find breaks in the next layer. It just depends.
Water...hmm...again no easy answers. Some scattered ideas: canyon bottoms are usually the easiest bet (depending on the canyon...some prior research is pretty essential) and often have water in the spring and fall. On benchlands above canyons, geology is helpful here too...I know the Navajo benches in the Escalante area or Robber's Roost are far more likely to have potholes than other formations. Cottonwoods can be helpful. If I look at google earth and there's zero green in the bottom of a canyon, I know I should be cautious. Reading prior trip reports or reliable books (Steve Allen) is helpful.
Overall, like anything it's a matter of building a toolkit of skills/experience/knowledge over a period of time. I'll also say that my experience is 95% on the Colorado Plateau. The last couple winters we've backpacked in southern Arizona and Big Bend, and while much of the above still holds, a lot of it is completely different. The diversity among deserts is pretty staggering.