So I made a glass platen out of two "floating" frames that I found at the local crafts store. These are picture frames with two glass panes and no backing. You put whatever you want in between the two panes, and it "floats" in the middle. The two panes together measured 1/8", which is nice. So I removed the panes, cut the frames so that they would join up at 90 degrees, put the panes back in, and ran a small bead of clear silicone (intended for waterproofing doors and windows) along the ends of the panes where they came together (so they don't fall out!)
I decided to try using two drawer slides on either side of the platen:
Here is a close-up of how the frame attaches to the slides. I had to be very delicate when drilling the holes for the bolts, since I would be drilling the triangular 3/4" MDF through the side.
However, I discovered that because the platen is a bit flimsy, you have to raise it by using both hands, one on either side! That's not the point of a movable platen!
So I think that next, I'm going to try something similar to what the Smithsonian Institute did, which is to attach the platen on either side to levers which go to an axle. I would turn the axle, by means of a crank or (later) a motor, and it raises and lowers the platen not vertically, but along the path of a circle: