I have the model just before yours the 355BHQ and I was told by PrimeTime to NEVER use slide out supports!!
I have not had that problem with my slides. I am not sure what you mean by sag but if you are referring to sag of the floor then it is most likely on your dinette super slide and the floor has been stepped on while it was closed. This will pull the screws out of the dinette bench where it is attached to the floor and will then sag.
While I don't have the auto leveling system I do put my rear stab down and then put a set of jacks just behind the rear tires of the coach and raise them to just touch the frame to keep the tires from bouncing. Otherwise my JT strongarms work very good.
IMO you will not totally eliminate the movement in your trailer unless you level it on blocks (like a mobile home) and remove the tires.
Otherwise we love our trailer too! we don't use the Jackknife sofa for a bed so that has not been a problem for us.