Although the frequency is shifted the distant image will still travel at the speed C.

Consider this.
You are going to measure the speed of light by measuring a distance it traveled.
Your ruler is made out of compressed light photons which you call matter.

If you put your ruler along a photon path in a strong gravitational field the light path will be measured as straight because the ruler will bend with the photon path. You will also bend with the ruler and so the ruler will seem straight.
( Remember the ruler is made of photons.)

If you are accelerated to an extremely fast velocity then your clock will slow causing the speed of light to remain at C. Observers who have not accelerated with you will see your ruler shrink in the direction of motion. These modifications to your clock and your ruler will cause a measured photon speed to remain at C.
( Remember the ruler and you also are made of photons and will change as the photons change.)

Your error is that you think that you and the ruler are “solid” and your time remains constant and it does not. We change with the photons because we are photons.

This is proven by the equation E = M * C^2

That is why the speed of light remains constant.

Energy and mass are the same thing in different forms and therefore will have some similar properties.

The reason that we humans reject this is because we think we are the center of the universe.
We expect that the universe must be considered with respect to us and our whims.
We think we are GOD.
But we are not.

This is why we are willing to reject reality even when experiments have proven what reality is.

This of course is only my opinion.

The speed of light has been measured many times and has been verified to a very exact value. No measurable deviation has been found larger then experimental error.

If you wish to comment on one of the statements here please copy and paste it into your post (in side brackets like this ) so I will know which statement you are referring to.

Duane