(I'm still floundering with the website) I don't see "scale" as relevant. I agree - the normal dimensions can be of any size, and the higher dimensions are shrunk (as you say) down to very small. The normal space is said to be changed by mass - particularly large concentrated masses (forming black holes). The higher dimensions are talked about as shrunk --- from any size down to Plank sized
Space - with its 3 dimensions (+ time) is distorted by mass --- no mention of changing dimensions. Possible extra dimentions (beyond the 3 +1) are considerred to only make sense if the dimensions are "wrapped up small" --- no mention of changing space. Why the different approach ?