I went to a fabric store and bought some black matte fabric. I then took the unassembled frame pieces and wrapped the fabric around the front, stretched it tight, and stapled it to the back of each piece. I also wrapped the cloth around the mitered corners and stapled that back, so in the end I had a black, fabric-covered frame piece. Then I assembled the frame using angle brackets, and stretched the screen across the back with the viewing side face down so that you look through the frame at the screen.
It came out beautifully.
My next attempt will be to build a masking system. My plan is to build a new frame with open slots in the top, bottom, and sides. Then I'll flush-mount from drawer rollers or teflon slides inside the frame, and attach some metal or black plastic solid sheets to those. That'll basically give me what looks like two sliding doors, except on the top and bottom.
The back of the frame will have a hole drilled at locations for 1.85:1 and 2:35:1, and I'll insert one of those switches that you can slide something over (it looks like a little ball and is spring loaded). Then the 'doors' will be connected to some hardware to allow a motor to open and close them. Perhaps a worm gear or something. Then I'll be connecting the switches to my automation controller. The idea is that when I press the button on my remote for hte proper aspect ratio, the controller will send an X-10 signal (or flip a relay using a 5A relay module) that starts the motor. The doors will then open or close until they hit the limit switch, which will cause the automation controller to turn off the motor.
This is all preliminary - I may find reasons why this won't work. But it looks like it should. To get the grooves in the wood frame for the slides, you can use a router, or find some wood that already has the grooves in it. Or, you could use regular wood and put some aluminum rails inside the frame for the doors. There are lots of ways to do this.
If you want a manual system, it's even easier. Just put some locking pins in your frame at the right positions for each aspect ratio, and drill a corresponding hole in each panel. Then just pull the pin out, move the panel to where you want it to mask that movie, and push the pin back in again.
You could make a system like that by just using a blind roller at the top and bottom of the screen (or sides for horizontal masking), and put some hooks on the screen at the proper locations. Then just pull the blinds down from the top and up from the bottom and hook them on the appropriate hook for your aspect ratio. But you'd have to find some pretty wide blinds, or make your own and make a rollers by using counterweights instead of springs for tension.