Well, since I need to get webmail of some form up and running, I went ahead and installed Squirrelmail for the time being. It worked perfectly without any modifications to the config actually. So, as far as I can tell, I believe Dovecot is set up and running correctly.
Edit: I was wrong... looks like Squirrelmail went ahead and made some folders of its own. The folders I had set up weren't under the inbox. That must have been the issue.
