Consider that although the Bible is completed much later than the Zayit Stone there's not necessarily consistency in the alphabet used in these poems (e.g. Psalm 145 is missing a letter (נ) in the Masoretic text but not in the Dead Sea Scrolls). I recall another example but it's not coming to mind.
So the fixing of the order of the alphabet started as an early process with competing orders. There is some possibility that they might have reordered some of the verses in these acrostic poems to be consistent with what they thought of as the correct order (even though the poet might have worked with a different order). This is mostly conjecture, but it shows something about our desire for order (even if the order is arbitrary), possibly as a teaching aid, and that we might retrofit things to this order.
Does this answer your question?