Our 5th wheel is about the same size as yours and we stayed at the North Campground (no hookups) at Bryce Canyon NP without any problem. A nearby campground with full hookups is Kodachrome Basin State Park--we also stayed there in a pull-through site. Obviously a longer commute than from the North Campground, but doable if you have to have hookups.
We tried to stay at Fruita CG at Capital Reef NP, but they were repaving it. So we stayed in Torrey at a FHU RV park newly renamed Wonderland. Not a bad park, but lots of road noise.
With a 5th wheel traveling US 89, keep in mind the tunnel rules going into the east entrance of Zion NP. You may have a long wait getting through it, depending on the size of the crowds while you are there. We had reservations for Watchmen CG at Zion, but didn't stay there after seeing our site (we couldn't have fully opened our slides). We ended up at the WiilowWind RV Park in Hurricane, but it was a really long commute. Of course, it was Memorial Day weekend. so beggars can't be choosers!
UT 12 is a GREAT road for scenery and shouldn't be a problem for someone used to towing in the mountains of West Virginia. Of course the trees block the view of the vertical drops in WV. But there are few trees in southern UT, so you can see the all the way to the bottom--on both sides of the road!
Have a great trip!