I think this would work ...
TT | Stamp & Punch Store & Go | Scrapbooking, Cardmaking & Craft Room Organization products
You can also search for the double-sided one (check the depth).
The vinyl is very clear, the inner trays are sturdy and close to the top so (if full) there is little to no shifting. If shifting is can issue, and If space allows, you could store them flat and stack them instead of using them book style.