In the third exam, I used Entangle to get over the abyss and did not get the Move Along Home achievement. I got it when I redid that exam on my next playthrough and used Long Jump. I was just reading the event guide and noticed that it said this about that exam:
Wed, Nov 20
Hopscotch exam. You'll need to find some illusion walls and hidden pathways. At least one dark square hides a hole. There are achievements for teleporting with the rune circle or going over a hole (jump, force push, entangle).
So I just wanted to let you know that if Entangle is supposed to count for that exam achievement, it does not appear to be working.