Hi,
as far as I can tell, there's no built-in functionality to get a full plus code list for an arbitrary area. However, I implemented something like this a while ago, using a scanline algorithm typically used in computer graphics. I haven't looked at that code for years, there might still be one-off errors around the edges, but it generally works.
I just generated this list of full plus codes from the coordinate list in your KML file, I hope it helps.