It strikes me that the school system is working back to front.
If it is the PARENTS that request the time slots with various teachers, then only the keen parents will attend.
Those that a teacher needs to talk to will not book a slot (or if they do, they will not be allocated enough time)
I also work in a youth organisation, we work the other way around,
it is the teacher that requests the parent to attend and gives them the time slot.
Kids with no issues do not get requests sent to parents except to turn up and they can ask questions in the milieu at the end
(Also we don't do the whole lot on a single day)