Been a while, '08 IIRC, we did it in the reverse, West Yellowstone to I-90 on our way to Glacier, no problems that I can remember, decent road with no severe grades.
We even saw moose on that route, which we never did in Yellowstone or the Tetons.:)
2007 Forester 2941DS
2014 Ford Focus
Zamboni, Long Haired Mini Dachshund