What’s the right tool then?

This looks like a pretty fun project and in my rough estimation a fun hacker project.

The right tool would likely be some conventional autopilot software; if you want AI cred you could train a Neural Network which maps some kind of path to the control features of the drone. LLMs are language models -- good for language, but not good for spacial reasoning or navigation or many of the other things you need to pilot a drone.