You are not reconing, you are refoaming. Reconing involves replacing the cone. Now to your problem. Yes, you should redo the first midrange. The reason is that having two surrounds on it will cause greater resistance to movement, which means it will likely not be outputting the right level for a proper balance of sound between the midrange and woofer and tweeter, and also not be right between the left and right speaker, since you are (hopefully) doing that one right.