Not counting the holodeck?
I've greatly enjoyed your work and I'm a little surprised you never saw "Edge"..! It should help flesh out a few things if the rest of your research hasn't already accounted for it. It was REALLY early on in the series, but it showed more of what the TARDIS looked like before the Doctor arguably got real experience with the universe, which could color subsequent iterations of the ship.
My view on what a TARDIS is, versus what it looks like, is that it's essentially a big box of Lego with which the operator can build whatever they want to internally AND externally. Sure, it comes with a big instruction manual detailing what it SHOULD look like as a default, and it even comes built in one way. But as with all things Lego, you can easily start tinkering with it, shifting blocks around and making it your own - heck, you can even lose pieces. Subsequent models of TARDIS are like the more modern Lego sets; new pieces and others that perform more specialized tasks or doing the same thing in new and interesting ways, but not taking away from the inherent customizability of the basic blocks.