Velodyne uses dual voice coils to improve symmetry electro-magnetically, sort of like the way the shorting ring does. They also use a servo feedback loop.The push-pull method is used to make pneumatic symmetry by using two drivers as conjugates. In one direction, the magnet attracts the voice coil and in the other, it repels. With two push-pull mounted drivers, on each half-cycle, one will be a little stronger and the other, a little weaker. Together, the force is the same.
The concept of inverting the magnet and the voice coil polarity is interesting. It would appear that you're trying to do the same thing - The idea being to cancel harmonic distortion using a conjugate pair. Sounds like a very good idea to me.