If we take our cue from the grain of the Bible as we find it in Gen.12:1-3, I suggest we think of the Bible's authority as its divinely given capacity to "author" communities who look like Jesus. This means that we will not first look at a church's theological statement to see if they have an adequate view of biblical authority. Rather, we will look at the way of life they pursue, the disciplines they practice, the quality of their community, and how they act to spread the blessings of God to the rest of the world. Doubtless the theological views of different communities will continue to vary but we will learn to read their lives in a way that we can discern whether they possess a "family likeness" to Jesus. If so, we will trust they are living "under biblical authority."
My view will doubtless seem too weak to some, too judgmental to others, and impractical to most. We are not well practiced at this type of discernment. But I believe we must learn this skill. This too brief and still evolving vision of biblical authority has important implications in other areas as well. At any rate, I think we all need to struggle to find ways to learn to identify and affirm communities that live out that "family resemblance" to Jesus in spite of their differences in theology.