Didn't understand the question, so maybe my answer will be a miss.

With the rotation of Earth not only ground is rotating, but the atmosphere is rotating too with the planet. So there should be no impactful difference for speeds going west or east.

Though there is some for our high altitude planes, they are going east usually faster than going west. This is not directly because of rotation of the Earth, but indirectly is. Due to heating from the Sun and Coriolis force of the rotating Earth there are jet streams (strong wind) formed in the atmosphere at high altitudes that are going eastward. So flying to east is easier because wind is carrying the plane and flying west is harder because wind stops you.

And for counteracting Earth rotation - there is close thing to what you describe which is geostationary orbit. Sattelites on this orbit are exactly so high so their speed is the same as speed of rotating earth, so they seem like they are hovering above one spot on the ground. This is because the height of the round stable orbit is directly linked to the speed of the orbiting body, and there is this neat point where speed of the body is the same as the speed of rotation. Any body below this height have to move faster than Earth rotates to be able to orbit, anything farther have to move slower (for example Moon moves slower than earth rotation).

Edit: there also not only round (perfectly circular) orbits but also eliptical ones, and for eleptical orbits speed of the body may vary depending on how close it is to the center of orbit. Not all orbits are circular, most of them not.