Thanks Lincoln, but looks like I can't do this because it will always be treated as "Basic".
In class.entrycon line 769 there is this hard-coded array:
if (!in_array($RegistrationMethod, array('Closed', 'Basic','Captcha','Approval','Invitation')))…
Thanks for the details.
The problem is if I create a new registration type, it risks being obsolete/incompatible on the next releases of Vanilla.
But so far it looks like the only option I have.