You touched on a weakness by asking about the group policy editor, that is one component of windows that is hard to replace in its entirety. First understand that with Linux and opensource based solutions the administration is more than point-and-click, so more experienced administrators will be needed.
We had a previous question about comparative services on https://www.linux.com/community/forums/system-management/active-directory-alternative/limit/20/offset/0 , I highly recommend for you to read that discussion to see various options.
Now as for replacing the entire domain, as an educational institution that change would require giving up your windows based software and potentially ms office. Due to that I would recommend looking at the potential of replacing the network servers and student facing machines with Linux and open source implementations and consider keeping the administration on windows, this is also recommended because many of the administrative users are set in their ways when in comparison the students are faster learners of technology and can easily adapt to the change in software.
Please post specific follow-up questions for specific software or service based questions.