We have the same tow vehicle ('11 limited 4x4 5.7L), but are towing a smaller rig (189FDR, 2,600 # dry, 19' long). I use a 12k equalizer. I tow around 65-70mph, and on all our trips i can rarely ever tell the trailer is there. On the interstate occasionally i get passed by a big rig going 80mph or so (much too fast) and my whole rig will move a bit, but not much. Certainly not enough movement to cause any concern.
Now, i think the important thing here is my rid is several feet shorter and weighs some 1,000 pounds less than yours, so take that into account. I'd still expect your setup to be similarly worry free.
2006 FF 189FBR | 2004 Jeep Grand Cherokee 4.7L HO