Since no amount of searching seems to be turning anything up, figured I'd post here.
So, it turns out the latest Plex Server update is no longer compatible with my version of OSX. It would have been nice if the updater had checked for that first before installing, but thankfully the updater keeps all installed versions on file. All you need to do to roll back is the following:
Go to ~/Library/Application Support/Plex Media Server/Updates (if your home library folder is hidden, go to Finder->Go->Go To Folder... and enter the full path).
There you'll see a list of folders with various version names. Within each version folder there will be a folder called "packages", containing a manifest file and a zip.
Copy the zip somewhere (ie, a temp folder) and decompress it. You'll be left with a folder called "Contents".
Find the Plex Media Server.app file in your Applications folder, right click it and select "show contents".
Delete the Contents folder within the app, and copy the newly unzipped Contents folder there instead.
Run the application.
You should be back up and running your previous version of choice.
Hope this helps and is not too redundant. Why there is no longer any option to install older versions of Plex Server is beyond me - the minimum system requirements just suddenly changed and there's no official way to go back.