5. Enter Administrators and click on "Check Name". This will validate the name and make sure the system is able to find it
6. Administrators should now be underlined, which means everything is correct and the group has been validated. Now you can click OK
7. Click OK again to get back to the screen in step #3. Now repeat steps #4-6 for the group named "Users", and also for "LOCAL SERVICE"
8. That's it. Close your policy editor and now any standard users using the computers affected by the policy should be allowed to set the time on those systems.
Thanks go to this post for pointing me in this direction. I'm still looking for a way to allow users to change the time zone too, but from what I've been finding it's not possible and you have to script it through AD instead.