I don't think it is related to the head coming up to speed at all. The waves will still be there but reduced as the overshoot is reduced because it reaches the corner more slowly. If it is doing an X move then the wave is created by the previous Y move. It is a property of everything in the universe be it central heating controllers or speedometer needles on cars, they all suffer from it and it cannot be cured, only minimised.

The proper way to minimise it would be with PID controllers on servo drives that have feedback. That would be one expensive printer.