Hi Lou, welcome.
The
Copernican Principle is not one that I have studied, but I understand it to simply mean we, as a planet/solar system/galaxy are not all that special. I'd bet that Copernicus would disagree with this view, however. His model was superior to Ptolemy's as it gave the universe a true center which was one motive for him. [Actually, Copernicus placed his center near the sun and not at the center of the sun. Ptolemy's model had a different orbital center for each planet offset from the Earth which he called the equant.]
Further Copernicus realized the elegance he found in his heliocentric model because his showed that as you move to the orbits of the next planet away from the sun then the orbital period increases; he had discovered a nicer order. It further resolved some other issues, but, unfortunately, the math for his model was about as difficult, perhaps a little worse, than the Ptolemy model.
I don't think I'm helping you much, but I thought I'd stir the pot a little.
Nevertheless, it is a reasonable principle when compared with any view that holds our planet and life are unique. Obviosly, if our planet were at the absolute center of the universe, there would be a lot more spin on how we view the universe and our uniqueness. [sorry 'bout the pun being it's your first post.
] Yet, our knowledge of the variables within the Drake Equation is hardly able to demonstrate that mankind is not somewhat unique or entirely unique. So, I suppose the Copernican Principle would have to be taken in the context it is meant. [Others will quite possibly disagree with me, so give 'em a chance.]
Please link to the ZV Effect (I failed to Google it down). Do you mean the Sunyaev-Zeldovich effect?
There is an
old thread regarding AIG's claim that may help you.
If their (AIG) argument is for Geocentricity then you might like to see a more recent and more robust debate about it in
Galileo Was Wrong.
The argument I like best against a rotating universe is how unlikely its rotation would be behave in such a jerky manner. Using quasars and interferometry for accuracy, scientists measure the changes in the rotation rate of the earth. Accuracy, IIRC, is good to about 20 mas (milliarcseconds) as determined by those at
IERS. The shifting air masses will cause significant mas (milliarcsec., not mass) variations daily. So, why would this air mass shifting be causal to the rotation of the entire universe. It is more plausible by far that it would be causal to the shifting of our planet instead.
Ultimately, you can not use science to crush a subjective belief, but you can influence it to some degree based on the strength science can bear, as well as, the amount of exposure the belief has to that science.
TalkOrigins does a nice job refuting many Creationists views.