After getting CUPS to accept my username and password, I moved on to the last root-only web interface standing, i.e. webmin.
Webmin's import feature is pretty sophisticated, as you can specify permissions for subsets of modules and users via the concept of webmin groups.
This implies that you first have to create such a group before you can import UNIX users.
Groups can be defined in the Webmin->Webmin Users module, I called mine "admins" and gave the members every permission available.
I then converted my UNIX user to webmin, checking the box "Use same password as unix user in the future" and assigned the admins group.
Apart from the "create group first" point, pretty intuitive.