About how long do you expect it to take to play this?
(More to the point for my purposes, could it reasonably fit into 30-40 minutes?)
I don't think it could, honestly.
Depending on how much your group gets into roleplaying the scenes, I'd expect a game to be anything between 1-2 hours. I believe you could play it in 40 minutes after a few runs once all players are familiar with the mechanics, and you decide to be brief with the roleplaying bits.