I couldn't really read your original post too well, but I can read your more concise post better. I'm still not sure what you are saying causes a gravitational redshift, however.

If it is the galaxy it is emitted from, then that redshift will be limited to a few parts in a million for a star, and perhaps one in a few hundred thousand or so for a galaxy, and it will have no relation to the overall distance travelled, once far enough away, since almost all of that limit will be reached when it is closer to the point of emission. It would also blueshift again slightly when approaching our galaxy, solar system, and planet.

If you are referring to the entire universe as one great sphere of mass, where the gravitational redshift depends on the gravitational potential between one point and another, then this would create a redshift or blueshift depending on our position in the sphere and that of the point of emission, and all blueshifts from points further from the center than we are, which we don't observe. Also, according to the Big Bang scenario, all points can be considered the center, so there is no particular direction for an overall gravity to act.

I'm not sure if either of these is what you meant, though, so you can let me know.

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