Hello denbec, to answer your first question, we chose to go over Beartooth Pass for the simple and possibly silly reason that it is almost 11,000 ft and we knew it would be gorgeous and epic (which it was). 14A naturally followed as the apparent direct route across N. WY. Honestly, we didn't notice that Big Horn pass was actually longer and steeper until the day before it. We probably would have gone the Greybull/Shell route had we realized that it would be less crazy. Going west, however, it will be less of an issue for you. No regrets here though, it was still a phenomenal experience.
Our route through Norris, Ennis, & Cameron was following Adv Cycling's Transam Route. We met our friends in Ennis because it was the closest point on the route to Bozeman. Hwy 89 to 12 would probably be a good way to link up to the N. Tier; I haven't been that way. There were some significant climbs on our route between W. Yellowstone and Missoula, but all worth it. It is spectacular country. You may want to consider Adv Cycling's Great Parks route from Missoula to the N. Tier. Either way, you can't lose. Best of luck to you. My advice to you right now is to take as long as you possibly can on your trip. Don't worry about the most direct route, follow what's interesting to you.
