I need some good inspiring ideas!
What about a washing line affair? Hold the cards in place with small pegs.
I would get some black foam core, and built it so it will stand up on it's own. Then just use Blu-Tack on the back of each card to hold it in place. You would still be able to open and close each card, but blu-tack is made to be easily removable without damage.
You half-decent with legos? That could perhaps be sorta crafty and cheap to free, depending on if you have any laying around.
Something like this: https://www.instructables.com/id/Make-Your-Own-Greeting-Card-Holder/ or maybe something like this https://www.instructables.com/id/Photograph_Display_Board/You might also consider building a small set of stepped shelves and stand some of your cards up on them.. Just two or three steps could display a lot of cards while keeping them almost fully visible.