I have no idea what the answers to my "security questions" are -- if I ever filled those out at all, I almost certainly just pounded my fists on the keyboard until the prompt went away -- and the alleged option to reset them using my recovery email address does not exist. Apparently the only recourse at this point, despite having two verified email addresses and a credit card in their system, is to call them on the phone and speak to some flunky like an animal.
So no 2-factor for me, I guess. Well played, Apple. Well played.