My post was somewhat tongue in cheek, and I agree the relativistic effects are negligible at normal aircraft altitudes and speeds, which is an accurate decription of the physics knowledge of most of the posters on this thread.
Since we are clearly talking about the Earth as a fixed frame of reference, its spin is irrelevant. If you are going down that road what about the fact that the Earth is moving at 18.5 miles a second around the Sun in its inertial frame, the Sun is moving in the Milky Way's inertial frame, etc, etc, etc! Take your pick - your aircraft can be doing any speed you like if you pick the right reference frame.
Speed only has meaning when it is related to a reference frame, which in this case is that of the Earth's surface. My understanding of aircraft "groundspeed" is the component of tangential speed at right angles to a radius drawn from the centre of the Earth, averaged over the distance of the route. Yes the start and finish points may have different elevations in terms of distance to the centre of the Earth, but nevertheless that is what groundspeed to a pilot is. Nothing more and nothing less.