The geometric argument against this remark is almost absurdly simple.

If we are moving along a line toward a point, and a galaxy alongside is moving toward the same point, we will converge with it. No fancy calculation is needed to show this. A simple sketch will do.

In your model a galaxy out in front would be pulling away from us and would be redshifted. One behind us would be lagging and also redshifted. The ones abreast of us would be blueshifted, with the more distant ones more strongly so.

The multitude of galaxies would be "spaghettified" upon approaching your reputed gravitational attractor.

If I am not mistaken, much the same thing has been said earlier in this thread. I recommend that you slow down, take a deep breath, and pay better attention to what is being written by a lot of well-informed people.