Get some Hockey Pucks and screw them to the cases from inside with some self tappers or something relatively strong fastener.
Apply four pucks per side so they'll grab the rack, whatever rack, at the four corners.
Shave the bottom pucks a little so as to add a lip that will rest on the rack tubing.
Get somebody to weld a piece of square stock bar to a piece of all-thread, so they form an "L"
Drill holes in the upper pucks so the all-thread will go thru. Position it so it grabs the rack tube with the square stock bar, and tighten it down.
Its a Zega case style technique rip off.
I bought a pair of these same boxes to do the same thing, and then my girlriend bought me the Zegas, becuase she didnt want to see me suffer.
I thought about mounting some 1" angle iron to the cases to grab the rack tube as well, but I never fleshed out the idea.
"Why BMW? You like to suffer? My sister, she has five kids, no husband. You come over?"