I am trying to authenticate but it seems that my approach is not working. I am logged into the administrator account, so I obviously know the admin password, but I can't authenticate in Finder or any other place that requires unlock. I am running the latest macOS High Sierra.
Based on the list of accounts, it appears to be that you're not an admin and there is no admin account on your computer. You'll need to create an admin account by running Setup Assistant again.
Boot into Single User Mode ⌘ + S.
Mount the drive by typing
/sbin/mount -uw /then ↩ enter.
Remove the Apple Setup Done file by typing
rm /var/db/.AppleSetupDonethen ↩ enter.
Reboot by typing
rebootthen ↩ enter.
Complete the setup process, creating a new admin account.