Will this (and can this) ever be fixed, or will I be better off handling those manually?

Again, for better readability . . .

As they appear on-screen:

• 01 - Trip Preparation
• 02 - The First Five Days
• 03 - "I Just Can't Do It."
• 04 - Glacier Plane Ride
• 05 - Wrong Way Round!
• 06 - Untitled [Interview]
• 07 - Thoughts After the Trip
• 08 - The Dusty Road and Charley's Puncture
• 09 - Claudio's Story
• 10 - Jimmy's Story
• 11 - Ewan Talks About the Title Track
• 12 - Untitled [UNICEF Information]

As they appear in the DVD menu:

• 01 - Trip Preparation
• 02 - The First Five Days
• 03 - "I Just Can't Do It."
• 04 - Glacier Plane Ride
• 05 - Wrong Way Round!
• 06 - Interview
• 07 - Thoughts After the Trip
• 08 - Ewan and Charley Talk About the Dusty Road and Charley's Puncture
• 09 - Claudio's Story
• 10 - Jimmy's Story
• 11 - Ewan Talks About the Stereophonics Title Track - Long Way Round
• 12 - UNICEF Information

In short: On TMDB, both order and spellings are off, title 12 is missing entirely.

I invite you to read this previous content report.