It seems that moving the seat forward or backward effectively changes the seat tube angle. The KOPS procedure seems to be a very reliable 'safe' point, so long as your cleats are positioned correctly with respect to the ball of your foot.
Moving the seat forward effectively increases the seat tube angle, and basically puts you in more of a TT position. A more forward position is good for steady spinning and areodynamics, but is less comfortable and not especially suitable for power changes (e.g. sudden accelerations).
Moving the seat backward makes for a more 'slack' seat tube angle, which is more comfortable, and is better suited for hill climbing and such, where lower cadence power changes are needed. It seems many (if not most) prefer to be seated a little further behind 'neutral' than forward where general road use is concerned.
In any case, moving the seat forward or backward will change the seat height settings required to get the same angle of knee extension. A simple goniometer and plumb bob can be very help where getting optimum seat settings is concerned, and even a small adjustment in the right direction can make for a significant change in power output.