A lot of hospitals won't schedule inductions on weekends. The hospital I delivered in last August would not. My OB had me pick a date at my 38w appointment in case I went over (I had my choice of any weekday between weeks 40 and 42, but could not go over 42), so it would be on the schedule. I picked 41w, but it wasn't needed as I went into labor naturally at 39w5d.
Also there are different types of induction...if you're already 2+ cm dilated, they usually have you come in early in the morning and start pitocin. If you're not at all dilated, or 1cm, they can have you come in at night for cervical ripening gel (Cervadil) or a foley bulb.
I would think Jill would be trying some natural induction methods by now as well (nipple stimulation is a great one, but I wonder how she feels about it given their repressed culture?). Castor oil isn't recommended anymore as it can cause the baby to pass meconium in utero.