I picked other because "No, they do not adhere to the Catholic Church, but they do hold office. (Thesis-ish)" was not quite what I would say. The problem is that some in the Novus Ordo do try to adhere to the Catholic Church despite the leaders, like the FFSP and ICK, (I know, some of their priests are traditional and some of their priests are modernist).
I think that what we need is a firm leader, who is fierce as a lion for Truth in public, but soft as a lamb when counseling individuals. (I stole that from how someone described +Williamson recently.) All these ideas are interesting to discuss, but a future Pope will have a lot of work to do in putting the Catholic Church back in order.