Additional assignment-related features and issues within Microsoft Teams for Education
Dear Matthew
I suggest you to create a ticket in the admin center, due to you have an school tenant, you can create a service request, support team is able to analyze what happen with Teams when you try to distribute an assignment.
So in any internet browser go to following link:
https://admin.microsoft.com/#/homepage
Access with your admin account, then in left pane click in Support > New service request > create a ticket, then in no more than 30min an agent will reach you by phone and will offer a remote session to understand better the issue.