I followed your middle option, Nebraska 12 a few years back and enjoyed it. Just west of Springview I turned south and followed dirt roads through the Niobrara National Scenic River Preserve for most of the final stretch into Valentine. I was riding a mountain bike on that tour. Ponca State Park is a good stop for camping just sightly off route a bit west of Sioux City. Niobrara State Park is on the route further west.
Niobrara National Scenic River (U.S. National Park Service)