Thanks so much, guys. I appreciate it.
Here's what I think you're telling me. Please comment further if I have screwed it up. If it is correct, should I add it to the wiki?
I want to build a new Wordpress website in a test subdomain, then transfer it to the regular domain that already contains other subdomains and web-based applications.
Old website - http://www.oldsite.com
Test website - http://www.test.oldsite.com
1) Using One-Click, install WordPress into http://www.test.oldsite.com.
2) When done, rename oldsite.com to oldsite.com.old
3) Make an empty oldsite.com folder and install a new WordPress One-Click. This is just to fool the system that there's a WordPress at oldsite.com. Now future WordPress one-click updates can be applied to the new location since you just replaced an existing One Click with a different one-click.
4) Rename the new WordPress oldsite.com to something like oldsite.com.wp and then move test.oldsite.com to oldsite.com.
5) Rename test.oldsite.com to oldsite.com
6) Create an empty test.oldsite.com folder (or just delete the subdomain via the panel if you're not going to keep it)
7) Go to the wp-admin for your site and change the URL Settings