The point is that there is no need to tweak GR. For example, [1] shows how properly accounting for GR and using rather detailed data about Milky Way allows to explain the rotational curves.
But GR is complex enough to allow very different behavior depending on the initial conditions of galaxy formations. So it would not be surprising to see different scale of deviations from Newtonian mechanics depending on Galaxy history or age.
One more thing. It is not true that stars simply fly through. Already in the second-order approximation in GR there are forces that behave like Lorentz force of electromagnetism perpendicular to the line of movement. Granted this a small effect, but on the scale of millions of years it matters. That alone can explain a lot of subtle behavior.
But GR is complex enough to allow very different behavior depending on the initial conditions of galaxy formations. So it would not be surprising to see different scale of deviations from Newtonian mechanics depending on Galaxy history or age.
[1] - https://arxiv.org/abs/1810.04445