Just thought of something: if I sew two solid arcs together, cut 'em up, and re-piece them together then the arcs would end up smaller length wise because of all the seam allowances of the units. I'd have to create a new solid arc template that factors in the seam allowances of the separate units. I'm thinking that might be trickier to sew since the seam allowances would probably turn that arc into a half circle.
But this method would probably work if one were to make a non-pieced version (two solid fabrics, no indivual units).