The most hideous drill for learning to push effectively, as taught by my dance coach, is to start at the goal line of the rink, push once, and make it all the way to the other end.
It requires that your one push be off the edge of the free blade with a deeply bent ankle, with a slow rise to a perfect, erect, still posture that doesn't wobble on the blade AT ALL, and utilizes the free leg to help balance, all the way down the rink.
I can usually get past the center (but that usually includes hitting a bunch of bumps and ruts on the way down the ice).
He strongly feels that I should be able to do it on either leg!