If the cabinets are 24 inches deep, just lay your 9 X 20 inch pieces straight in. Pile them up in colour family and If you keep your 6 inch ruler handy, you can slide it into the pile, lift the top fabric and pull out the fold you want.
The other option would be to make mini bolts standing up but do them 2 deep. The problem with that is you would need to remove the front fabrics to see the ones behind.
Save the top shelves to store your batts.