The thing is, your proposed change to the scale has to work exactly like "invisible stuff on the scale." So, we can observe dark matter in the early universe with the CMB, we can observe it in the large scale structure, and we can observe it in rotation curves. And the results of these observations is, that dark matter has to behave like matter, just dark. So your proposed new theory would need to deviate from standard theory in precisely the way an additional matter component would.