Are you saying take 18-N then 56-E? Looks like a much longer drive than just going back to the 15.
Yes, there's a diagonal cut off between Enterprise & Newcastle that goes along the hill behind some farms - shortens it a little. And yes, it's definitely the "scenic route" - iow longer. For a even longer jaunt, go thru Snow Canyon on your way out of town (again, if you're headed north from the SC)
not short cuts, alternatives, and Beaver remains well within range.