The shake and wiggle up front is from the side to side, front to back movement of the landing legs. The longer extended the more pronouced the "wiggle".
Robfla, you might want to consider another set of scizzor jacks to take the bounce out of the rear of your rig. I put a set just behind the rear wheels on each side and that takes my suspension out of play. With our long rigs the flex and bounce will still be there even with the stabilizers.
As for the leveling system I think the bounce will be elminated due to the 4 point stance. As for the "wiggle" you might be better off with a tripod on the king pin. I don't know if you could attach something to the legs of them. You may not need it in the end.
I can try to push my rig with the stabilizers engaged and cannot budge it. Sat through TS Irene last season with 45-50MPH gusts and barley moved it. The key is getting them engaged right which took me a few trials but now I know the procedure and get it right every time.
2014 375 BHFS Eagle Premier
2014 Ram 3500 Longhorn DRW CC
6.7 CTD, Aisin, 4.10's