So just a moment ago I managed to install MediaWiki, the software project which drives Wikipedia, on a LunarPages based web site (this one). It turned out to be fairly straight forward. Here’s what I did:

(1) Downloaded MediaWiki v1.6.8. (Newer version require a newer version of PHP, and the version currently running on the LunarPages servers is 4.4.)
(2) Unpacked and copied the entire MediaWiki folder (mediawiki-1.6.8) into the public_html directory. Renamed the folder to ‘wiki’.
(3) Using the MySQL account maintanance page, created a new database (username_wiki1) and a new MySQL user (username_wiki1), and added the new user to the new database, giving the new user full permissions over the database.
(4) Loaded the Wiki site (chaosinmotion.com/wiki), then followed the directions. Because the database is already created in step 3, you don’t need to have root permissions or anything like that.
(5) Follow the rest of the directions, such as moving the LocalSettings.php file to the wiki directory.

I think MediaWiki looks a lot better than the phpWiki software that comes with LunarPages.

Now I just need to copy the content from the old site, and I should be up and running.