Allowing specific contacts always but allow all contacts for a limited amount of time

I'm trying to figure out a way to allow my child to message anyone during the app limit set for messages (1 hour) but once that limit is reached to be able to message specific contacts only. I can't seem to find the right combination of settings to allow this. I am forced to either block messages completely at the end of the time limit or allow messaging to anyone until downtime via the schedule set.