Out Of Hours SMS Alarm Notification

We have a system where all medium priority alarms are only sent via sms between the hours of 08:00 and 17:00, outside of these hours the alarms are only sent via email. This is currently working fine.
Our customer now wants any still active unacknowledged alarms to be sent at 08:00 so that the operator can get notified to their phone as soon as they start work. I’m having trouble figuring out how to do this as there is also escalation, i.e. at 08:00 it should start from the first contact in the list.
Is it possible to do this?