You're going to paint it? *Why not heavy paper or light weight cardboard?

That would work (I think it's basically what paint-grade edgebanding
is), but where can I get a single strip 200 inches long?

I wanted to have one seam (on the back side) rather than three
distributed around the perimeter. I don't know how I'd bend Luan and
plastic laminate would always be trying to come apart at the seams.