In the WSLVT system, we advocate pivoting on the
heel... as opposed to turning on the balls of the feet, whereby your balance is constantly shifting and causing you to actually move
away from the target, when in fact the aim should be to remain close enough to strike with full power and remain
closer to the target. Hope this helps

DMP
Over the years I've worked in two WC lineages. The first advocated simultaneous foot pivoting on the heels, while the second system (the one I've remained with) advocates using the
center of the foot. I also work with an eskrima group that does some similar footwork using the balls of the feet. I believe all three can be effective, although each method has certain advantages.
On the other hand, I don't agree with you statement that pivoting on the balls of the feet
"moves you away from your target". What moves you away from your opponent is
shifting your center of gravity. If your system favors a 50-50 weight distribution then pivoting doesn't move your body much to either side, regardless of how you do it. If you pivot on your toes, you may see a bit of a shift, but only an inch or so--depending on your posture. By contrast, if you strongly weight the rear leg using a 70-30 distribution, or a nearly 100-0 distribution (as in the system I train) you will see a dramatic side to side movement when pivoting. This does increase the distance between you and your target... but
that can be a good thing. If your opponent is driving forward with a lot of force, we use our pivot to absorb the force and slip aside, going off-line like a bullfighter out of the path of a charging bull. With this line of thought, the ultimate objective is to borrow the opponent's force,
letting him make your pivot and press you aside like a bent spring. Now if you are stronger and faster than your opponent, you might not bother with this.
As for
Poor Uke, the trick to turning on the center of the foot is the weight shift. This method is works well with the systems like WT which advocate a total weight shift (nearly 100% on the rear leg) and a sequential (one leg at a time) pivot rather than a simultaneous pivot. With this method, you shift your weight to the side, and then turn the unweighted foot, eliminating the friction problem. When turning from side to side the legs flow in sequence with the unweighted leg starting the motion, turning into YGKYM and the other leg picking up the motion and turning out as your weight flows across to the other side. The movement is fluid like a wave. Also, the turn is motivated by the knee... not the foot. Rather like the elbow turning the arm in bong-sau, the knee turns the leg here, and this really reduces joint stress. On the other hand, if you do not turn with a strong weight shift, that is if you prefer a 60-40 or even 50-50 approach, I would not recommend this method.
BTW
David, after reading your post, I actually went over and set up my stance in front of a spot on the wall, extended my arms pointing at the spot, and tried various methods of pivoting to check out the whole distance thing. The observations above seemed to hold up, or else the walls are moving again... in which case I'm going to have to seriously adjust my drinking habits. --Steve