If you want a compromise, then keep all of the other setup process and automate the actual calibration -- set a time that it takes to do an accurate calibration (say, 30 seconds), and give that a small CEP (not perfect, but close), with shorter calibration times giving a larger CEP (i.e., the calibration point being off in a random direction by a distance proportional to how much you shortcut the calibration time). Once the calibration is complete, everything else functions as it does now -- you turn, it throws the calibration off until the sight stabilizes, changed wind angle throws off the calibration, changed speed or altitude throws off the calibration...
This wouldn't remove the necessity of keeping your plane stable at your calibration course, altitude, and speed; it just eliminates the finicky detail of having to track the ground with the scope, handwaving that as being done by a crewman who knows what they're doing.