To answer your question about TV, it is relatively new is laid out very well in my opinion. Add Antelope Canyon to your stops. It is just north and east of Page, there are three outfits to serve you. There are two on the right left side of the Hwy going toward Monument Valley. The one closest to the Hwy is in my opinion is the best.
The construction in Arches is supposed to be conducted during the day, but you know how that goes. The big campground will be closed during construction but a much nicer one is a State Park at Dead Horse Point.
I know how you feel about seeing all you can and you can see that area but I'd read about it a lot and narrow stuff down. You can drive over from Vegas to the GCNP and then over to Page, the up to Monument Valley and the up to Blanding UT to see Muley Point, Goosenecks, Natural Bridges, Mexican Hat, CanyonlandsNP, Upper Colorado River, Arches and more. Five days of driving around once there and three days from GC and then up to Bryce and Zion. I suggest Blanding because it is easier to find space there during school vacation. So now you have five or six days left for Bryce and Zion. There is so much to see up that way.
Oh yeah, Mary at the Monticello Visitors Center has a lot of great ideas. The others there are pretty good but Mary is fantastic. Monticello is also a good place to home base for that area.
Enjoy and if you're like most you'll be planning your return on the flight home.