First,
I think Monsterhearts hits its sweet spot much quicker than Apocalypse World does. Sessions 2 & 3 are where the gold is, as opposed to Apocalypse World's sessions 4 & 5 (in my experience).
That said, here's what you can do to get to the juicy drama right away:
1. Create a seating chart in advance. Maybe make it 5 desks by 4 desks, and fill about 14 of those desk (out of 20) with students. For each, just write something like "Felicia, total psycho, biker" or "Rodney, closet drag queen." The Seating Chart is where lots of prime drama gets its seed, but it also takes time to make. Making it in advance works, and all you need to do is say "Okay, PCs, where do you sit? What do you think of hte person next to you?" Done.
2. Consider pre-generated characters. It works best if you pick most of their stuff in advance, and let the player sit down and pick one or two final things. Pick their look, origin, stats, and most moves. Leave them to pick name & 1 move.
3. Finally, I'm writing a con scenario pack called The Blood of Misty Harbour, right now. It's a three-episode miniseries. Each episode plays out in 2-3 hours. Each episode has some new pre-generated characters and a set of opening scenes & guiding questions. It's like a story-gamified adventure module. I'd happily let you see the playtest copy, and you could run the first two episodes to see how it goes! DM me your email address if interested.