I bought a white-finished particle board shelf and cut it into strips. Then each valance got one of the strips glued to the back, using Gorilla Glue (because of its tremendous gap-filling property), held back from the top of the valance by 3/8" to make room for the LED strip lites. The strip serves as a stiffener, as a means to retard warpage of the relatively thin valance panels, and finally as a lite reflector for the LEDs, directing their lite back toward the cabin side and upward.
|Back side of a valance panel, top edge to the bottom of the picture|
Unfortunately, because of the size of my workspace, I can only deal with the valances from one side at a time.