It took over a week, but I finally figured it out! I have resolved all of the permissions problems that were driving me crazy and now have what appears to be a fully-functioning Wikidot server running on my home network. Through this process I have learned a lot more than I planned, but it was a great feeling when the final attempt actually worked without errors. Those "A-Ha!" moments are great! ;)
I just posted a how-to: Wikidot Home Network install
The steps documented have been confirmed to work on 3 different PCs. If you can run Ubuntu Server 7.10, the rest should be pretty easy now.
The how-to still needs some follow-up, but it's far enough along that you can get a working Wikidot server going in a couple of hours.