Okay a few things you can do, I did and it helped a lot.
check out pics on webshots.
first, put jacks or stabilizers just in front of front tires to take bounce out of suspension system. I land mine on frame then go up about 1 inch
second, don't let the stabilizers down all the way, like standing on tooth picks, that does not help with any sway.use blocking to keep it up higher to body as this gives stabs a wider stance like standing with your legs far apart compared to standing straight up with legs together, more stability.
third, wheel chocks, small plastic ones, or make some of your own, or can buy one step chocks from rv dealers.
I built mine and use a lot of force with jack screw against tires. Zero front back movement
fourth, can buy Jt strongarm sway controls that bolt to frame and bottom of stabs.
there are ways you can get the sway and bounce out. just depends on how much you want out and how much you want to spend. With trailers and suspension you will get some, just part of trailering.
http://outdoors.webshots.com/album/577456038uQWrsP. also pic in there for back cupboard I added for storage
http://outdoors.webshots.com/album/572781145jUsGSk
blocking and pic of back room before adding cupboard.