The problem is how to start a conversation.
We had a similar problem in the university. At the beginning of the semester, the students have to register for a Moodle server with additional material. So when they create an account, we have to send a few thousands of confirmation emails in a short period out of the blue, that makes Gmail/Yahoo/Outlook/Whatever unhappy.
The solution was to ask the students to send an email to the server half an hour before registering. It's not ideal, but it adds us to a secret list of known contacts of the student, so (most) emails are delivered.
Why are you making the students use their personal e-mail rather than the school e-mail?
> we have to send a few thousands of confirmation emails
What are you confirming, and why do you have to send it as E-mail? If it's sign-ups, just "confirm" using the same system that the user used to sign-up. Presumably HTTP.