Hello Josiah,
A little late, but I just wanted to tell you I have something similar, with the difference that I wanted a list of random titles shown in one tiddler. The idea was to create random connections and generate ideas when opening the wiki.
I used one of the many great plugins made by Tobias Beer :
http://tobibeer.github.io/tw5-plugins/#random and I added this to my opening tiddler : <<list-links filter:"[!is[system]random[3]sort[title]]">> .
For what you want :
- Get the plugin from Tobias' page
- Put this filter in your Default Tiddlers section from the Control Panel : [tag[xyz]random[3]sort[title]]
This should give you 3 random tiddlers tagged xyz and sorted by title when you open your file. Of course, you should play with the filter to adapt it to what you want (more tiddlers, different order etc).