myname+website@gmail.com should absolutely work -- please file a bug if not: https://github.com/mozilla/browserid-sideshow/issues/new
EDIT: Now I remember my use case.
My email is actually myname+randomstring+website@otherdomain.com, and so I want to sign in with the same randomstring every time. Previously when signing in to Persona with my Gmail email address it would suggest all alternatives, and I'd choose the appropriate one. Now it logs in with Gmail directly instead.
Of course, this is such an edge case that it's probably not worth doing anything about. And I can simply sign into Persona with myname@otherdomain.com for the previous functionality.