So I've finished off the majority of the code rewrite. The game now correctly displays planet squares in the new system in all three screens that show them. Now I just need to add a few more things to the planet editor and test it a bit.
I've still got thousands of image tiles to go through and get into the database, so that's still going to be a real chore. I can just dribble those in for now though.
I also realized that I've got to do all of this again with the Asteroid Squares now. Sigh.