OMFG the latch wasn't broken.

I couldn't tell why I couldn't attach the "replacement" latch. Turns out I just hadn't attached the ribbon correctly in the first place and I managed to yank it out while the latch was closed.

After borrowing @Not_mermista's phone as a makeshift magnifying glass, I saw that the original latch was still there and I had been trying to install a "replacement" latch on top of the one that's already there.

Anyway, everything works now again, my shoulder buttons are great, my touch screen is great, back to Professor Layton I go.