Real G,
Your suggestion worked brilliantly! Definitely going to keep it in mind in the future. It's super easy to do, too.
My hobby shop had some glass fibre cloth, which I cut into strips and then covered with a layer of CA. One layer gave me enough strength, but the great part about this method is you can do it as many times as necessary. In hindsight, I probably shouldn't have spent the extra money on the glass fibre cloth, as paper towels would have done the job just as well.
If there is a "trick", I guess I would just recommend not "soaking" the strips too much. There were a few places where the CA didn't have enough material to bond with, and still hadn't dried 24 hours later. I spread a bit of baking soda around on it, and it hardened instantly.
Anyway... Now that I have a solid base to work from, the rest of Moonbase Alpha should be much more enjoyable to work on.
Incidentally, I've decided to mount this effort vertically on the wall, since it's 18" x 18". I absolutely don't have that much horizontal space anywhere, but I can probably negotiate with the wife for a section of wall out of the way somewhere. ;-)
Thanks again for the assist.
Mark