You have yet to address one of the most important points I've made. We know that the interior of the sun is exactly analogous to the IGM. Both are gasses filled with electrons and protons. Both have incident photons. In the sun, photons interact with the electrons and protons and scatter in a random direction. There is no prefered direction of re-emission in the sun. Your propose a similar case for the IGM. You propose that the IGM is filled with ionized hydrogen (which it is). Therefore, the IGM is filled with protons and electrons just like the sun. However, you propose that the photons that interact with the IGM are absorbed and re-emitted in the forward direction almost exclusively. This is decidedly not the case in the sun. In fact, it is the exact opposite of what happens in the sun, since in the sun photons are re-emitted in a random direction. Since the two situations are almost exactly the same, you have a very big task: explain why photons in the IGM are absorbed and re-emitted without change in direction, while in the sun they are scattered randomly.
What makes you think that the photons in the Sun are not forward scattered as well as Compton scattered?
The Sun is very dense and the optical path must be very large compared to the IGM. There is a theory by John Kiernan who showed that redshifting occured in the arms of the Sun. I will try to find the paper if you are interested.
Photons are undoubtedly forward scattered. However, they have equal probability of being scattered in any direction. If photons in the sun had a much higher chance of being forward scattered (as your theory requires), then the random walk time for photons out of the sun would change, and this would be quite obvious. Photons in the sun are scattered randomly. They have no prefered direction of scattering.
