One thing to keep in mind with "Father's Day", for the "empty" TARDIS shell, the reason the interior looked like it did was because they assembled the box inside-out, so what we were looking at while the Doctor was standing inside the shell was, in fact, the outside sides simply turned around.
And with the above references, maybe we should refer to this as the "2005 TARDIS". Almost everyone seems to call it the "Tennant" TARDIS (and I admit I am also guilty of this sometimes), and forgets that it started out as the "Eccleston" TARDIS. And Christopher Eccleston is the one who brought 'Doctor Who' back to the screen. So calling it the "2005 TARDIS" would give credit to both actors, especially since they essentially used the same "box".
As to the design of the inside, when the crew isn't using the backdrop of the console room on the rear wall, they've got a green screen insert so they can put the TARDIS interior into the scene in post production. As some of the TARDIS assembly photos in the Reference section show, the inside walls are indeed flat, and painted black. (So was the Classic Series TARDIS prop, and this can really be seen in the final moments of "The Three Doctors" when everyone has returned to Earth and is talking outside the TARDIS with the 2nd and 3rd Doctors; both TARDIS doors are wide open and the interior, though painted black, is lit enough that you can even see the block-outs on the back wall's windows.)
Dino.