I'd encourage you to deviate north a bit from doing KHII KGUP direct and fly over the Grand Canyon. It's quite a site to behold. Maybe stop in at KGCN if you've got the time. Make sure you've got the special Grand Canyon charts if you decide to do any flying in that area. If you have good high desert experience, consider checking out Bar 10 (1Z1). Aviation101 did a video on that on youtube and it looks like a breathtaking place to fly into.
I've done a little bit of flying in the high desert, and here are some of the considerations I've had related to flying there. I don't know if you've got a lot of experience out there or not, but if you don't, here's what I considered going out there. If you *do* then I'm leaving this for folks that don't, and I'd love to hear your high desert flying tips!
Minimally, you'll want to consider weather, high altitude operations, and things to help with emergency survival.
Weather: Time of year can change quite a bit in terms of how much weather you'll have to navigate around. Make sure to have plenty of alternate airports in mind in case thunderstorms or other inclement weather pops up in your route of flight. If you don't have ADS-B In with NEXRAD on board, I'd recommend considering getting one of those devices that give you access to such. Make sure you're comfortable talking to Flight Service during the flight and getting up to date weather reports to check your thinking against. Carry extra fuel to handle potential weather related deviations.
High Altitude: Make sure you do your density altitude calculations and consider carrying less weight and/or flying in the early morning to avoid the worst of it, especially when leaving KGUP. Leaving early can also help reduce the turbulence you generally get later in the day in the high desert. If you can, get some time with an instructor doing high density altitude operations.
Survival: The route you've planned can be fairly remote in places. I'd encourage you to file a flight plan for each leg and make position reports along the way. Also carry the usual basic survival gear in case you go down in the desert. Plenty of water, a first aid kit, etc. One of those personal locator beacons can be really handy if you don't have time to get a position report out before a forced landing. Possibly consider making sure your route follows major highways so that finding help is easier.