Hi Andrew,
It's great that you want to take care of your internal customers too! As you know, this can be an effective way to boost morale and increase collegiality amongst departments. The monthly meetings would be a great place for the reps who participate in "walking in the student's shoes" to share their experiences and insights.
I'm sure your team will appreciate the opportunity to come together to enhance the customer service experience internally and externally.
Great plan.