The gravitional curvature alone is not all that determines gravitational time dialation. Imagine a large hollow massive sphere. As you approach this sphere the gravitational time dialation will increase as you approach this sphere. If you pass inside this sphere then spacetime will be flat inside, yet the time dialation will remain slowed to that of the surface anywhere inside the sphere. Under GR the depth of field determines relative time dialation not the curvature.

Now imagine two observers seperated inside this sphere and the mass of the sphere is steadily increasing. Inside the time dialtion will steadily increase compared to a far removed observer even though the spacetime inside remains flat. Now when one of our observers sends a light signal to another the signal will be redshifted because of the finite value of C. The second observer will recieve this signal at a later time when the spacetime interval has changed. This is where I get the time dependent Hubble shift zh=(ωo-ωe)/ωe.

The question this posses is, "How can we speak of the Hubble expansion being an expansion of space itself if it has no relation to the spacetime interval?" If we assume the relationship is direct then it leads to this problem with proper distances after a period of expansion. Note that for our sphere the radius appears to decrease for our two observers because our sphere is not expanding with the spacetime.

Your questions are very much appreciated.