plastigue
IHMO it is not the cardboard part of the cards at all but the plastic coating/lamination; how thick the plastic is and how long it may have stayed in the laminating machine. If one side of the plastic is shrunken more than the other, it could be almost impossible to 'permanently' flatten them.
With extensive use, many of us find our favorite deck is curved in the direction we shuffle; what we have done through many years of shuffling is stretched the coating on one side.
Perhaps instead of merely placing a heavy tome on top of them flat on the table, you could consider bending them in the opposite direction by placing the short ends of the deck up on something with space underneath, then placing something heavy in the middle of the bend to push and hold it in the opposite curve- stretching the plastic in the opposte direction?
Have you tried using fanning powder so they slip easier?