Bigger base plate for the little slots, giving increased area of contact with the laminate to spread the load.
Fix in place with double sided carpet tape, and a couple of small screws into the laminate - just to ensure the sticky tape doesn't "unstick" when it gets warm.
If it doesn't work the tape will peel off under gentle pressure and the screws holes will hardly show, and on the inside anyway. Then it's on to Plan B, or C or . . . .