I eventually figured out a few ways to give myself root. The passwords in the password file were not hashed. First method was to spoof the login prompt. Ran it remotely from another computer on another computer that I knew the teacher would always log into. Once I succeeded in getting root's password, I put another method into one of the boot up scripts which would copy the password file somewhere else if another file was present. All I had to do then was just reboot a computer to get root's password. Later I was able to figure out the memory location where the group and user number was stored by comparing the memory dumps while being logged in as various users. Then I just needed to poke those memory locations, start a new shell, and I was root.
It's a shame that these computers have kind of disappeared. They are a part of computing history, for Ontario at least. I've contacted a few people online that still have hardware. Everyone seems to be unwilling to share what they have.
To preserve the history, I think it would help if they could be emulated. Even a modern web browser probably possesses enough computer power to emulate them. They ran on a 286, at least the early ones did.