Welp, as near as I can tell my cluster of a script does exactly what I'm looking for. I've updated the Pastebin link for those who are curious (https://pastebin.com/0JvUrzQU).
It will analyze existing group memberships and remove users if they do not meet all of the following requirements:
The account no longer matches the specified $fileString
The account is disabled
The account does not reside within the $searchBase
Next, it will pull all accounts from the system, excludes existing members, and adds the remaining users to the group if they meet all of the following requirements:
The account is enabled
The account matches the specified $fileString
The account resides within the $searchBase
The sAMAccountName does not contain a 1 (something we use internally)
The Display Name does not contain the string 'test' (we do not have any users who have 'test' in their name yet :-D)
After the above is done, it writes the changes to a log file (which is overwritten each time the script runs) and if emails it off to a specified email address.