Have you thought of just adding a soft valance to hide your new rods?
a. a one inch rod pocket type valance is very light and you can make it the length needed. The bottom of the valance could be straight or shaped depending on your taste.
b.Nearly anything you use that is wooden will be heavy or it will possibly warp.
c. Is it possible to change out the existing rods for a decorative rod that is supposed to show?
Good luck
N.