Might I just throw out some epic driving/riding locations that are close to your route.
Zion to Paige, AZ (the vermillion cliffs area is epic especially if you catch it around dusk). The other good thing is most the roads are decent. If you go all the way down to tuba city you can then cut back up to Four Corners and then to Durango. I've made that drive a number of times and something about being on the indian reservation that is peaceful, can be kind of boring straights in there but it is meditative.
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The million dollar highway from Durango to silverton (most amazing twisty, epic mountain ranges, green forests, amazing views). And if you are going in June the weather will be good, maybe still a slight chill at AM and early evening. The 145 that you had posted on one of your maps from cortes up to montrose is I would say just ok but nowhere near as awesome as the 550 out of durango through silverton. I would put it on comparison with driving through the Great Smoky Mountains, and Blue Ridge Mountains.
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The 84 through wyoming, idaho and then down into Orego/WA is pretty scenic. There is one point where you come out from I believe La Grande Down the mountain to Pendleton that you are looking down over this amazing valley floor from the side of the mountain as you drive down. Makes you feel kind of small in the grand scheme of things.
BTW the I-5 south of Oregon kind of sucks. Not to be mean, I think I've made that drive 3 times. Each time I honestly remember just driving as fast as possible to get it over with. There is only one section called the Grapevine Ascent that is cool, but I think that is way south of where you are going.
I would avoid I-90 through eastern WA, boring drive there too. And actually much of the Montana drives that I remember were just long straight shots. Some nice views, but just butt soreness inducing go sessions.
Of all my lowly opinions I would say you definitely have to do the Million Dollar Highway, It woudl only maybe add 45 minutes to an hour to your trip. And Durango is one of the best towns the States have to offer. Have dinner at the Durango Brewing Company, good beer and food.
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