The doctrine of "the Bible alone" is not a "red herring." It's the central teaching of Protestantism. It's the only doctrine that all Protestants share in common. I don't think, it's irrelevant. It's doctrinal junk, but not irrelevant.
Paul satisfactorily answers you but I doubt you'd listen to him on authority any more than you do on who the pillar and foundation of truth is.
Paul wasn't referring to the New Testament. How do I know this? Because the canon of Scripture wasn't settled until several Church Councils around the year 400 A.D., many centuries after Pauls death.
New testament and cannon are our words. Paul spoke to this by referencing his own writings and the writings of the other apostles in charging to keep to what they taught in word or in writing. He then specifically deliniated what those things were so there would be no question. Paul did answer it for you. You just choose to excuse yourself from that course on the buffet as though it is your right to choose what you will heed or not. It is, actually your choice, but it's God's right to judge you on that basis because you know better and have the ability to know better. And pointing your finger at the church of Rome in the presence of God won't save your hide anymore than pointing at Jimmy swaggert would save Hugh Heffner's.