Also, on the note of .edu domains being restricted to post -secondary institutions; that's not entirely true. That wasn't the original rule, so some non-university level schools are grandfathered in and own .edu domains. For instance, my high school has a .edu domain.
Once you see a domain that's an educational institute it gets whitelisted and further registrations from that domain get ok'd.
No matter what text you include there, you're gonna get the odd student registering with a hotmail/gmail/yahoo account (I've tried something similar in the past). Try and get a list of free email accounts to give feedback on those straight away.
I think any domain using the .edu TLD is safe straight-away, but I'm not from the US, so it may be worth clarifying that.
you could automate this quite easily, too.