Read-only scope for private email

I’m designing a single-sign-on integration with Github that requires the authenticated user’s email address which we are using as the identifier to tie this user to other SSO provider or our own user/password identity service.
To do this I’ve tried both read:user and user:email scopes because they are both read-only but neither can read a private email, which is very common among your user base.
What I see that LogDNA does is ask for user scope which is read-write but can read a private email.
This seems like an awkward solution.
I don’t need write privilege just privilege to read the private email, and in fact to read that and the user’s name.
Is there or could you invent a different scope for this purpose?