Your conveyor belt analogy isn't right. In order to see more lower spectrum (red) light, the star would have to emit more of it. Also, if the lower spectrum light traveled faster, it would appear disproportionately dimmer compared to the higher spectrum.
Why dimmer? Hmm...how do I explain this.
Ok you have two belts. One moving at rate X and the other moving at 2X. At the start of each, you have a guy who places a red photon on it at the rate of one per second. Now imagine you are at the end of each belt, what do you see?
The X belt's photons are coming of more densely packed than the 2X belt. Densely packed photons means more energy is striking your eye at any given moment, and therefore appears brighter. In order to appear just as bright as the X belt, the 2X belt guy would have to double his rate.
WARNING: NOT a cosmologist. I am but a mere chemist. I really don't know anything useful. I am willing to be corrected.
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Another thing to think about:
I plan on beating the rotating galaxy example to death, so bear with me.
Say we have two identical stars (sample spectum emitted, same size, etc) in the same galaxy that are both the same distance away from us. The only difference ... one rotate towards us and one rotates away. What would we expect to see?
In your theory, they would appear identical because they are both the same distance away.
In the Big Bang Theory, we would observe one red shifted and the other blue shifted.
We see the latter.