I actually figured it out. I think it was the same for the multitool all along too. I've been experimenting with it all day and was going to make a post about it when I could confirm.
I thought long and hard about what happened when I started seeing "better" ships, and then it hit me. I had just recently bought a new ship to fix the space station docking bug (it breaks the game). So I tried it again - I bought another new ship - and sure enough after warping to a new system and allowing the game to re-seed new ships, those new ships now were bigger and better yet again.
I bought new multitools many times over the course of my playthrough. I think THAT is what was improving them as I went, and it had nothing to do with center proximity. And it seems the more ships you buy, the better your ship options get. Which kind of makes sense.
My ship is now up to a 7x5 with mostly filled in modules. Will keep buying ships all day until I hit 8x6 for confirmation. Currently sitting in a station waiting for a passerby, because I've been hit with the space station bug again. Can't leave until I get to buy a new ship. Great. Been sitting here for 30 minutes now...
Also, weird thing to note - when you buy a ship, the ship upgrades relatively match the ones you have installed and it affects the price. So if you go ship shopping and want a discount, purge all upgrades off your ship (you'll do this anyway for the resources since you can't take them with you) and load a new system to refresh the ships. When you trade, their ship will be junk now too and much much cheaper. Works like a charm.