What the Assembly considered pure and authentic was based on insufficient evidence. One can only imagine what their thoughts would have been if they had known of the thousands of manuscripts that would be discovered in the subsequent two centuries.
This is is exceedingly problematic...I understand where you are coming from...but it's exceedingly problematic.
What you are looking for is a purely rationalistic argument for the establishment of the New Testament text. The trouble is, if you press that line of reasoning, you are left with an OLD TESTAMENT that we have no reason to believe looks anything like what it did in it's original form. In the Old Testament, many of the earliest copies we have are centuries older than the autographs and for some we are looking at more that 1,500 years!
If the text must be established upon rationalistic empiricism, there is no basis to accept that the Old Testament text has survived the stream of history without significant corruption.
The reality is, we accept the Old Testament not upon the mere broken reed of human reason, but faith. We believe it was pure in the time of Christ because he did not correct it and we have no reason to believe it was corrupted since then. On top of that, we believe that God preserves his Word just as it teaches in numerous places.
If we all accept the Old Testament text by faith (and we do whether we want to admit it or not), we need to press the faith argument in how we handle the text of the New Testament as well.