I've never used US 16 route from Buffalo, so couldn't guess (seem to remember people saying it isn't a bad route). Easier than US 14 from Sheridan from what I've heard, I believe.
I went up that way once, even took 14 A, wouldn't do it again. The 14 A part, It was a rush.
I-90 W to Livingston, then US 89 S to Gardner & North Entrance is an easy climb up to Mammoth Area. We used this route in 2009. Less climb than from Cody up & down into Yellowstone Lake area. But was come from North Dakota. Via I-94 W to I-90 W by Billings.
Eastside Routes Into YellowstoneMy Guess would be with your rig, you wouldn't have a problem. Seems the climb up from Cody isn't as bad as the climb from Fishing Bridge area to Cody. Should be a lot shorter route for you.
:CDesertHawk- Las Cruces, NM USA
*2015 Lance 1985~Casita de Campo~23' 4" Tongue to Bumper, Dinette Slide
160 watt Solar Panel/GoPower! Solar Controller
*2009 White Ford F-150 Reg. Cab
Long Bed with A.R.E. Molded Fiberglass Topper
*Previously~ 2005 16' Scamp