Well ahead of my initial TAS by a minute and 18 seconds so far, though I do expect to "lose" most of that lead by re-routing the Hunter Rank grinding.
Prologue: -765 (-12.47)
Chapter 1: -969 (-16.12)
Chapter 2: -1108 (-18.31)
Chapter 3: -1017 (-17.00)
"Collecting Tunes", "Wonders of the World", "Pest Extermination" and "Container Arrangement": -811 (-13.33)