The aircraft flying in opposite directions around the Earth are actually not equivalent to each other and thus you would not expect their time dilation factors to be identical. They are not in inertial frames. Rather, they are accelerating because they are flying in a circle. Acceleration is not relative. The aircraft flying with the Earth's rotation will complete the circle faster than the aircraft flying against the Earth's rotation will. This means that the aircraft flying with the Earth's rotation will have a higher acceleration than the other plane.
They are not in inertial frames.
Yes, OK. I also want to help. SR is valid for uniform motions. That is, fixed speed and straight path in accordance with Galilean relativity principle.
SR allow to assign local place/object/Earth for reference/inertial frame. And we may suppose the aircrafts on linear path for small time. And the atomic clocks have to indicate the same time.
However in GR, similar problems are ignored.
Yes your evidence is not support for SR by many reasons (especially, Vearth +/- Vairplane resultant speeds are clearly wrong);. It contains an intention of manipulation and misinformation. Some one may accept them.