My off the cuff opinion, with no real experience to back it up: The bike bags are likely to be catching the wind, increasing the swaying. I noticed, while shopping for racks, that Saris sells "Protect-O-Pads" to keep the bikes from contacting each other. Can't you just put the bikes inside the Grand Cherokee for the long drives?
FWIW, I have seen a lot of positive reviews of the T2 on the net. I'm sure you've done the search by now.