I resolved the sloppy box issue over the weekend. (get your mind out of the gutter!)
Van, your foam rubber idea worked great! That baby fits snug as a bug in a rug now. I is a happy motobricker!
I must admit....before crying out for help on the forum here, I never actually fastened the box to the plate, thus wasn't aware of how the rack contributes to immobilizing the box. All I had done was fit the plate onto the rack, realized how much the plate slopped around and bummed out. Before I embarked on the foam rubber mission, I fastened the box to the plate. Although the box did move around more than I thought necessary, it wasn't as much as I thought it would be based on how much slop the plate had on the rack. I now realize the plate requires generous movement to facilitate easy mating with the box and therefore the box to mate with the rack.
I found the exact package of foam rubber at Home Depot - about $8 after tax. I surrounded the perimeter of the box where it mates with the rack. Those two short strips in the middle, rather than stick'em to the box I chose to stick'em to the plate instead.
All in all it worked out excellent. I iced down about a gallon and a half worth of water bottles in my soft cooler, shoved the cooler into the box and rode all Sunday afternoon in the sweltering 97 degree heat. The water stayed frigid cold, the box rode nice and solid, and although the ride wasn't quite on par with the exhilaration of a 70 degree Spring day, I had a kickass time with nary a give-a-shit to be had. :-)
While I was stopped for one of my breaks, I realized I didn't have the box lid properly latched :mbird WTMF! I goofed around with it a couple minutes and learned its characteristics. My closing/latching technique is now perfected. I don't think I will have any trouble with the lid flying open.