My idea was basically the folios that we have dated to pre 600 which make up a near complete quran sounds like a paradox, but this can be resolved if we view these as the sources for the quran rather than the quran itself. Each community within the movement, abrahamist, jewish, christian etc would have had their own writings, largely apocryphal. These were not originally meant to be read together but separately in reading circles in each sub community. This was the state of affairs until at least the time of muawiya. But i think the sources were codified into a book, the Kitaab, by Abd al Malik in order to unite the ravaged empire after the second fitna. He combined books to unite each of these peoples who were all arab, but stationed in different parts (eg the Abrahamists were concentrated in Jerusalem and Damascus, the (post)Christian Alids remained in Hira, and a significant Persian element was re emerging in the east, etc.) All of these people contributed their scriptures to the formation of this Book and hence are called People of the Book (the book here should therefore be the proto-quran, not the bible). To emphasize this new united Arab identity he instructed his scribes to sift through the sources and record Signs, or Ayats, of God’s original covenant (or deen) with Abraham, to which the Arabs were heirs. This would unite them and shift the eschatological energy concentrated on Jerusalem to a more epxansive, empire building idea, to have «the Kingdom of God reign over the heavens and the earth» (usually translated as to god belongs the hosts of the heavens and the earth). Thus the Quran frequently reminds its readers that in these pages are signs which point in the direction showing that the Arabs, like the Jews, are God’s chosen people and can place their mark on history, found in the scriptures of the people who formed the original believers movement. Thus «these signs were foretold in the Scripture We gave to Moses and Jesus.» The signs are that the Arabs must submit-Islām- their law to God in the Abrahamic covenant, later misunderstood as Abraham originally supposedly being a Muslim.
Originally it would have been read not as a whole codified scripture much less one equal to the Bible, as Gabriel Said Renyolds remarks it essentially functions as a Midrash on the bible. You can only read it if you undersrand the Bible. Maybe it was viewed as something like an Arabic ‘Illiad’ or ‘Oddesey’.