If you are saying that we observe galaxies whose gravity is weaker than your models for the distribution of dark matter, then that is an argument against your models, not for them.
And here is why: If you have two galaxies with about the same size and about the same number of observed stars they should have about the same distribution of barionic matter. So gravity should work the same in them, no matter if that gravity is described by Newtonian theory (probably not), General Relativity (I would assume that, but who knows) or your modified theory of gravity (maybe, maybe not). Any difference between them can not be due to the theory of gravity. But it can easily come from different amounts of un-seen dark matter.
I don't see why the scenario "gravity works differently at large scales" couldn't explain the observations until we have some idea how gravity would work differently.
Don't forget that each of these observations rely on a quite large sets of assumptions about everything from how much luminosity from galaxies with a certain (normal) mass can vary to how we estimate distances to very far away objects. We don't have that many observations of e.g. gravitational lensing. And, if we realize we actually don't know how to calculate things correctly with GR, or our theory of GR is wrong, that will have implications for all of those assumptions.
The dark matter hypothesis might very well be right. It is a very reasonable guess. But so far I think the proofs for it have been overstated.
And I can say myself that not everyone agrees with that discovery: http://www.astronomy.com/news/2019/09/astronomers-cant-agree...
Well, people still debate about the Bullet cluster. But if it's correct then it's actually a good (relatively) confirmation for some sort of dark matter. It two similar galaxies look the same but have dramatically different mass distribution then there's some mass we don't see yet.