My claim is precisely that air travel along a due east-west axis will involve no coriolis forces, as there's no change in the distance of the plane from the center of the rotating body (earth). That's why I questioned the intelligence of the guy on the other forum who suggested it.
Assuming a perfectly calm day (i.e., the air is moving at the same velocity as the Earth), the plane flying from Tehran will have benefit of the fact that the Earth's rotation is bringing Tel Aviv closer to him, whereas the plane flying from Tel Aviv to Tehran will experience the opposite effect. Even artillery shells, which travel far shorter distances than airplanes, must have the Earth's rotation accounted for by their gun's guidance system if they are to hit their targets.
You're partly right! Under the conditions I described, earth's rotation would be cancelled out by a headwind hindering the first plane and a tailwind assisting the second plane, if they were both flying at haircut altitude. But most modern air combat operations are conducted at far higher altitudes, where the thinner air will exert less dynamic pressure against the speeding aircraft than will the thicker air on deck. Thus, the effect I mentioned will be observed.
Once again, great experiment! You're working out all of the corollaries of your theories. You're doing a thorough job. I like that.