I like your routing just fine, although I can't recall the section between Loveland and Ft. Collins. I've often taken 287 from Ft Collins to Laramie and from Rawlins to Moran Junction, likewise Hwy 14 from Greybull to Ranchester. They're normally good roads the whole route without unwanted surprises.
As 1mtnman stated, Hwy 16 from Worland to Buffalo is a little more gentle drive up and down the mountain, but both are good, scenic highways. Hwy 14 is a little more scenic during the ascent and descent, but 16 is more scenic over the top. Going from Cody to Sheridan would be shorter/quicker via Hwy 14, but if your destination is the Black Hills, both routes are about the same, maybe a few minutes longer via Hwy 14. You'll want to gear down for the descent on either route. (I'd avoid 14A with your rig.)
Welcome to Wyoming. Hope you have a great vacation!