Best Route from Sioux Falls SD to West Yellowstone?

The three tunnels near the Buffalo Bill dam west of Cody are very short and have plenty of height. No propane restrictions.

The East Entrance road isn't a nightmare by any stretch. It's just a long climb. No switchbacks that I can recall and going in you will be on the wall side of the road, rather than the steep drop off side. Route 16 up the east side of the Bighorns is also a long climb so you will have some practice. Use lower gears going down the west side.