I have very little experience with the PA-28, but I can tell you what works for me in a C172. Short field takeoff - Try your best to be ultra smooth with the backpressure. For an experienced pilot there will be no quick aft forward transitions on the yoke. In order to accelerate to Vy you will need to start with a lot of backpressure and smoothly decrease until there's no pressure, then to the point that you will need to push the yoke to remain in ground effect.
Soft field landing - If you need to decrease the amount of power to reduce float, then do it. Just remember, you can have some float with the soft field. It was also recommended that you choose an aiming point closer on the runway, another valid suggestion.
Short field landing - I treat these the same as a normal approach and landing. If you hit the target 50 ft. airspeed outlined in the POH on a normal approach and landing, the airplane won't float too much. I disagree with "dragging it in" as I discussed in the thread on mushing, but I'll leave that story for that thread.