Hi friends!
Recently-ish I move to my own appartment with my SO and bought a 5x5 IKEA Kallax to store all my boardgames. Picture attached.
Unfortunately some games are just too big for the Kallax, I can't store them neither vertically nor horizontally. For the longest time I've just had them just on top of the Kallax freely, but recently we (finally) got an AC unit and they would block the airflow.
Currently they're sitting on the floor but I feel sad for them :P
I considered getting a small Kallax, like a 2x2 or something and put them on top, but seems a bit overkill and I'm not sure it would be aesthetically pleasing.
i bought a storage ottoman - all of my board games fit inside. i don't have nearly as many as you do though, but it fits all of the weirdly shaped games and i can keep them in the living room area where they are used. the ottoman itself works great as a table for the games, with everyone sitting on the floor around it.