Method One: Use a Sliding Door Guide
My local home improvement center offers various sliding door guides. I chose 4' x 9/16" x 7/8" plastic ones. I found ones with two U-channels, but one U-channel is all I really needed. I also bought some 1" x 1/8" x 3' aluminum flat bar, some ¾" sheet metal screws, and some Silicone II Window and Door Sealant. I drilled two holes 2.5" apart in the 1 x 4 benchwork joists and the bars as well, then mounted the bars against my layout's end joists. Next I cut the plastic guides in half with a hacksaw so they'd be the same height as Walthers backdrops (2'). Then I laid a thick 2' bead of silicone on lines I drew on the back of the hardboard backdrops; I pressed the plastic guides—channels facing outwards—onto these beads firmly and let them dry overnight.
The next day I mounted the backdrops on the layout from the top. I had to make sure before I even began that there was slightly more then 2' of space between the top of the flat bars and the ceiling, so the backdrops could be lowered onto the bars with bar edges in U-channels. It was important that the bars were parallel to the layout and to each other, and that there was 1/16" of play so things weren't too tight for ease of use.
Other materials exist with U-channels, and lumber exists with pre-made grooves, and nothing is stopping you from sawing your own grooves into boards and gluing them to the backdrops. But it was nice to find pre-made guides that functioned nicely—I can recommend them. Also, iron flat bar exists and that would be stronger, but I didn't see the need for that.
Now examine fig. 1. Note that to have several backdrops in a row, you have to mount the flat bars on the layout and the guides on the hardboard in just the right place. One flat bar has two edges, each of which can be inserted into a guide channel.