Hi, what a nice trip you have to look forward to plus the Subaru is a great choice for your tarmac eating weapon !
Going on your mapping there is a few suggestions I would like to make.
1] From Phoenix to Grand canyon I would take 89 from Flagstaff past Sunset crater NM [a possible side trip] towards Cameron and enter the Grand canyon from the East entrance along Desert view drive with it's many viewpoints along the way. The first in the park is the "Old Watchtower" that has some wide open views of the Colorado as it makes it's way into the canyon and you can follow it's progress along the rim edge into the village area.
2] If you have the time cut further inland from San Fran and visit Yosemite NP, it's beautiful !
3]On leaving Yellowstone drive down through the Grand Tetons.
4] Time is everything but if you have enough to spare I would head towards Moab where you can visit Arches NP and Canyonlands "Islands in the sky2 section. If you were to do this you could head South to Monticello, Cortez and Durango where you will meet an amazing "drivers" road North back to Montrose called the "Million dollar highway" [550] through the old towns of Silverton and Ouray.
This was a great drive in the RV but I wish I had my old classic Subaru WRX to wind my way through the mountains !
US 50 through Black canyon and Currecanti is a good drive as well but another great road is the Trail ridge road through Rocky mountain NP that should be open by the time you hit those parts, although further North than you have planned.