Adjust the case not the cards
Have you considered putting a set of cabinet bumpers (little round silicone nubs) or furniture pads (felt rounds for the bottom of furniture to keep it from scratching the floor) to the back of the case at the bottom edge?
This should move the bottom of the case out away from the wall, tipping the whole hanging case back towards the wall and in theory make the shelves level for the cards to sit on.
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