I believe that the school has to sign up for UE4 in order for students to receive the free licenses. I tried this last semester, and the administration wasn't interested. Also, if you do end up going with UE4, you should check out this showcase asset. I used it in a previous project and it was a nice and quick way to…
That's definitely the way to go, sub to UE4, wait until the end of the month, unsub. Use that version of the engine until there's new features that really interest you, resub. Repeat. Also if you have a student email you can get it free for a year through Github.
Just to clarify on this, because OP mentioned them both, UE works like this (pay one month then cancel and you can keep using it), whereas AFAIK if you cancel a CryEngine sub you will no longer have access to it. UE4 is definitely the way to go these days :)