Newcastle (all one word -- hard to find as two) gives you US hwy 16 to SD hwy 79 or US hwy 85 to I-90 using major routes, with US 85 appearing to be longer, but I'm not familiar with US 16 or US 85 in that region, so flip a coin unless someone has more info. Just looking at a map I'd choose US 16, but I'd look a bit closer, perhaps a topo map or such.
We took US 85 up to NewCastle and 16 from there to Custer, and on to Rapid City to pick up I-90 on our way to Sioux Falls.
It was a decent run.
Though, we were at 30' plus tow.
Except for maybe a gas stop, or something, I don't recall anything on the road that might make a difference with 6' more on the RV.