Well, I've finally decided to upgrade this site to the latest verison of Drupal. The actual process of migrating to version 7 wasn't too bad. The majority of issues came from Views and fields not being named or typed the same way they were in Drupal 6. Changing all the views by hand was not that difficult and it allowed me to do a bit of how cleaning withing views. Views in Drupal 7 is sooooo much better!
The biggest challenge has been recreating the site's theme. Although the general look and feel is more or less the same as before, I have made some visual tweaks here and there. The biggest change has been the fly-out menu and the switch to a responsive, mobile-friendly layout. I'm still working on getting that finished, but for the most part the site looks good on just about any size viewport.
The only downside to the switch to Drupal 7 is that my host, MediaTemple's Gridserver, has performance issues with the new system. There are a couple of tweaks that help, mainly changing references within the database file from "Innodb" to "MyISAM." I have no idea what this does, but it helps keep the database from freezing up and timing out on the Gridserver.