Look at the Moki Dugway highway on your way from Arches to Monument Valley.
We did the opposite by going from Monument Valley to Arches so we had a climb. Going the route you go you'll be going down. Check out Valley of the God's at the bottom along with Goosenecks State Park. You'll be glad you did!
On the way to Monument Valley be sure to stop at the Forrest Gump spot... great view as you are heading to MV.
We did UT261 - I hated every minute of it, but she thought it was amazing. Lol forgot about the Forrest Gump spot - but oh well. Monument valley was beautiful, but the view was ****** up all week long. Hazy everywhere we went - arches, canyonlands, monument valley, grand canyon.. Wildfires. Hate em. Not only do they wreck the landscape, they wreck the view, too. Damn. Oh well. The only part of the trip that was a new stop for me (down south) was monument valley, and you could still see it well enough. I was impressed.