I read the books in chronological order, which revealed a significant change in maturity / logical consistency between the Quint and Twig Sagas. For a new read-through I would recommend sticking to the original order of releases (with the exception reading a lost bark scroll where it fits chronologically), as it more closely matches the development of the overarching themes in the Edge Chronicles.
Honorable Mentions:
If I had to add The Sky Chart, it would be D-Tier. If I had to split up the Lost Bark Scrolls, I would rate both Cloud Wolf and The Stone Pilot D-Tier. However, the The Slaughterer's Quest and The Blooding of Rufus Filatine would be on A-Tier, but since they make the larger part of the Lost Bark Scrolls, I kept it on A-Tier.
Did you love it, did you hate it, what would you rate it?