Hi Nick!
Two things: the horizontal walls - there's something off, you should see the bricks of the northen walls. If I understand correctly* than a horizontal wall that has no other wall to the top nor to the bottom should use tile (x:2, y:3). The tiles you mention are for like thicker blocks of walls (rendered as empty holes... idk, maybe I should had celing/floor there?
Second: Vertical ones. The autotiles pngs were created later than the picture you're refering to was made by hand (in Tiled iirc) using the tiles from the full tileset (0x72_DungeonTilesetII_v1.*.png).
I've just checked the Godot setup (couldn't remember, didn't look at it for a while :/) and now I recall that I had the same trouble and I gave up and just put the walls in the middle as you noticed. To fill the gaps I've provided the half-floors tiles in atlas_floor-16x16.png.
I believe what we want here is not possible with regular autotiles. I might be wrong but in any case the current setup is not sufficent. Meybe the "draw the floor" not "draw the wall" approach? IDK. (If you figure this out please let me know!)
[*] I'm always confused with autotiles. They are difficult to read to me and the setup is tedious, and yet they fail to do what I want and are super lmited otherwise. I'd rather go with a rule-base approach like ldtk or similar.