Thanks for photos, had replied earlier but lost what I wrote. Essentially that yes, using tape or some attached tubing to get the rack rod diameter thicker is the easiest way to remove any play. As the last fellow pointed out, you'll have to play with the tab thing at bottom to get it to hold properly.
Basically tab stopping pannier from moving in one direction, and then properly positioning the upper things so that one of them butts up against part of the rack stopping it from moving in the other direction.
Apply tab to lower part of rack first, then angled approach of the top bits, so it doesn't move one way or the other.
I'm sure you'll get it. Just muck around adjusting things.