As to authority, you suggest that a formal church hierarchy might have the ability to decide better than individual denominations as to proper interpretation… at least it seems an implied suggestion. But we know that in real history, this has proven problematic, which is why the reformation happened in the first place. The authority was not denied because protestants were anti-authoritarian, but because the authorities were clearly wrong, corrupt, and false leaders. So we know that not all roman catholics believed what the church taught, and many did not even know what they were supposed to teach. There may be one formal organization, but still many many streams of thought. At the time of the reformation, some of those streams of thought became new denominations.
This does not mean interpretive anarchy in the protestant side, since protestants too believe that individual interpretations are not valid unless validated by a group of believers, presumably a group of elders or teachers or leaders. So now I am a Calvinist, perhaps a former Calvinist, attending an anabaptist church. This demonstrates that while there may be many denominations, there is still something larger and greater that results in a unity, although a unity that is often fraught with difficulties. But who said life was easy?
The alternative, in spite of the difficulties, is that scripture is the authority, and Christ is the head of the church. The statement is simpler than its consequence, but nevertheless, it needs to be the starting point. Neither church, nor science, nor business, nor human desire, can take priority over the revelation of Christ in scripture, and this gives scripture an authority that nothing else can have.