Stabilising chaptered media from a Hero 2024

Hey all - a little stuck here, I'm sure others have had the same.

I have a little 2024 Hero, and I want to combine and stabilise the footage. If I stabilise each file using Player alone, it looks great, but because they're all handled separately, there are bad seams between the files when trying to combine them for editing.

I had assumed the official tools would combine and stabilise for me in Player, but I can't do that.

Any ideas?