Overall, I enjoyed it very much. Didn't like the traffic in Tetons/Yellowstone areas and in some parts of CO, like heading towards Breckenridge. I highly recommend the detour to Glacier. Going to the Sun is a spectacular ride. It would only add about 3 days to go off route, ride the west slope the following day, and then return to the NT route in the Whitefish/Columbia Falls area.
In addition to the WA passes noted, you will have other challenges. The route from Dolores to Telluride is a long slog up. Then you will have Dallas Divide, Monarch and Hoosier Passes. The latter two are over 11,000'. Strong winds in WY, Togwotee Pass at nearly 9,700’, and there is a long stretch (Rawlins to Lander) with few services. The climb out of Ennis, MT is a bear.
Rode the much of the TA between Missoula and Twin Bridges this past June (and in '11). The free cyclist-only Bike Camp in Twin bridges rocks. There is a good grocery store in town and a library with computers. Jackson Hot Springs, west of Big Hole Pass, is a nice place to stop for the night. They have rooms or you can camp. Either way, the price includes use of the pool (and a towel) which is fed by a hot spring. There is bar food and a more formal dining room. There is also a café across the street that I think serves Mexican food. Don’t camp in Wisdom unless you have some heavy duty mosquito repellant. If you do stay there (there is a screened picnic shelter in the park where they allow camping), The Crossings at Fetty’s serves up good grub and adult beverages. The climb from Wisdom to Chief Joseph Pass is long, but most of it is not steep. The Gibbons Pass Alternative is a relatively easy climb up, but the west slope was very bumpy/rocky when I did it in June. And it’s very narrow. If you are up for that sort of riding, the scenery is worth it. The store at the campground in Sula closes at 5 p.m. and has very limited groceries. Darby has a good grocery store and is a better option. The Old Darby Alternative between Darby and Hamilton is well worth the seven or so miles of unpaved riding and gives you a rest from U.S. 93. The road was in good shape when I was there in June.
An alternative to Big Hole Pass and Jackson Hot Springs is to take the Pioneer Mountains Scenic Byway, which starts on your right between Badger and Big Hole Passes. The summit is 7,900’, but only the last five miles of the climb are difficult. Then you get a very scenic 27 mile descent into Wise River. There are a couple of U.S.F.S. campgrounds with water along the descent but no food source. However, before the summit, at the Grasshopper Inn, which may or may not be open (It was this year when I passed through), you can go off route a short distance to Ma’s Country Store or whatever it’s called and pick up groceries there. Wise River has a nice bar/restaurant and a small grocery store. From there, you can head west on MT 43 to Wisdom to get back on route. This alternative is more effort but worth it in my opinion. The meadows you pass through during the descent are gorgeous.
I could go on a bit more, but I recently got back from a 9-day trip across PA and need to dig out from under some work.