There is no administration panel to manage users on CryptPad yet. So far our goal has to be that we want to know as little as possible about our users. It's a privacy principle important to us.
A future workaround (not possible as of today) would be to use the teams functionality. Blocking registrations on your instance as you did but create teams and use the invite links to have them join your instance.
For now, I created a feature request on our GItHub application repository to keep track and discuss this with the development team.
Sorry I wasn't able to give a positive answer to your question and your use-case!