After thinking about it some more, I decided to buy some 1/4"-thick common foamboard. This photo shows the 2' x 4' module that I built from cutting sections of foamboard and gluing them to the bottom of the layout surface using construction adhesive.
I put two more sheets of the foamboard on the top, because the whole thing was a bit too flexible. After painting the top layer, I started gluing the wooden ties for the module. This was to be one of the modules for the Canonsburg, PA coal tipple. I had read somewhere that regular white glue would transmit the wheels' sound through the ties and that one should use Mod Podge instead, as it remains somewhat flexible. So, that's what I did. Note that I put a sheet of 1/8" cork under the area where the track was to be. My experience was that Mod Podge made no difference, and so since it is more expensive than regular glue, I'll not use it for this purpose anymore.
I had glued 2" x 2" blocks of wood into the module's corners, and installed hardware so that I could screw in these legs that I found at the home center. This allowed them to be removable. I could sit at the module and work on it with my regular chair.
Things were progressing quite nicely and so I started hand-laying the rail. I wanted to go all out and actually glue the rail down on top of tie plates that I built out of styrene. The last tie was thinner so that I could glue a PC-board tie to it, and then solder the rail to that, to hopefully minimize any damage done to the rail if it was accidentally caught by a shirt sleeve. However, after giving it a good trial period, the obvious problem with this idea was the fact that the whole set up was very, very wobbly. One night I was trying to get out of the chair, and my foot accidentally hit one of the module's legs. This tore the corner of the module apart, and so, combined with the other issue, it was time to pull the plug on this experiment.