I have not read the whole webpage, but only the part describing the hypothesis of cosmological redshift due to the Shapiro effect.
As far as I know, a remote observer would indeed measure a modification of the speed of light when light passes through a gravitational potential, since it experiences a time-delay wrt to a trayectory through empty space.
But I am not sure that this will produce a redshift. To calculate the redshift due to gravitation one has to make use of the formula for gravitational redshift derived from a Schwarschild spacetime. This will lead to a prediction of redshift as well as blueshift when light falls into and comes out from potentials.
May be I am missing something.