If you are strong enougn, a tandem won't be a problem. I spent a week on the Trans Am route between Lander, WY and Fairplay, CO riding with a couple who were pedaling a BikeFriday tandem pulling a BikeFriday trailer. They dropped me going up Hoosier Pass, which is the highest point on the Trans Am Trail--11,500+ ft.
If you follow the Trans Am route, ride Yellowstone early as the map suggests. The traffic can be horrible. And when I was there 9 years ago, there were no shoulders on some busy roads, including the road between Yellowstone and Teetons. Hope they have improved things since then.
There is a good chance you will have to stop in Jeffrey City, WY. Somewhere at this forum a traveller who stayed at the motel in town had mushrooms growing in his carpet.
As for food, there is a good discussion on this page a few topics down.