Okay, while I think everyone's given up on this, I did find a solution, though I'm not certain of the cause. I reinstalled with yum (doing a remove, deleting all my web files, then reinstall) and reset the databases just to find the same issue.
After that, I deleted the web files again and downloaded the zip and installed that way. The themes showed up. As far as I know, the only difference between the two methods is that yum will locate the files in /usr/share which need to be copied, but the more notable difference is that the wp-config.php file is located in /etc/wordpress instead of the root web directory.
After the themes were working, I decided to set up the symbolic link to the /etc/wordpress location again, but after doing so I lost all the additional themes in the panel. After I realized that broke theme selection, I returned it to its original condition. This still didn't fix it, so I just reinstalled the downloaded file one last time and I'll leave it as such.
It leads me to suspect there's something with the symbolic link to the config file that is causing the issue, but it could be something with linux permissions, pathing, or even a bug. Removing the symbolic link should have fixed any of those issue if that were the case, so it could easily be something else causing the issue.
I'm going to go ahead and tag this thread as resolved, but I do think that someone should look further into the difference between the yum installed and downloaded versions. I could find very little information on this site regarding yum installation, so perhaps it's unusual or atypical that WordPress would be installed that way. However, since it is possible, it would probably be worth mentioning, even if this is the only difference between the two.