I don't think anybody has ever suggested a "choose whatever time you want 24x7" approach.
At 30 minutes per child and 20 kids per classroom, you're going to need a minimum of 10 hours. So you'll likely have to break it up over two days. Assuming evening appointments are out of the question:If you did Tuesday from 1:00-6:00 and Wednesday from 8:00-1:00, you would:
1) Allow more "desirable" time-slots: some early, some late to accommodate different schedules
2) Would give people a choice of days in case there's a reason they can't come one or the other.
3) Would give your teachers a lunch break -- and perhaps a sanity break, because I can imagine that an entire day of listening to the same book over and over without breaks would be difficult.
I think most reasonable people would understand that not everyone can get their first choice of times. But if you give people some options, they'll do their best to work with you.