>polarity shouldn't make a difference since it's just a magnetic pull

 

Good point, the math for that isn't as simple as saying when the current reverses so does the force....it would if the projectile were permanently magnetized (and that were the significant effect) but it is just iron and its own magentization is caused by the coil and reverses too. If that did happen, one could try to tune the circuit to oscillate just once and pull the projectile partway then push. But as you say, by the time the projectile is at the midpoint one wants to have the current shut off.