When we first got our camper I use to drive with the sun visors down,
the campers nose moves alot in relation to front of truck. Normal yes, frame flexes/twists between bed and cab but after a while you wont notice.
A rubber mat, even with the spray in liner will help alot if there is actually movement. 
As to rocking, not sure. Center of gravity is a lot higher so truck will handle/react different to any side forces. If camper is actually rocking in the bed, really not likely given weight of camper (11' under 2000#?) better tie downs could help. Unfamiliar with Brophys other than the old stake pockets. Umm I just looked, 
crbrophy.com I think Id start saving for Torklift or HappiJac tie downs.