It's not a good idea, in my experience to put your games or consoles/deices anywhere that has no climate control, I would not recommend the garage, attic and especially not an outdoor shed.
I recommend buying a deeper shelving unit, (tall and skinny sized) that can hold more games while taking less space, I also recommend re-sorting your collection to video game genre. but that is my setup. I myself have a sizable collection of various games, all my collection is sorted by the type of game it is, for example FPS games are on a dedicated shelf and I have paper signs telling me where they are stored, since I don't have a display at all.
The Immortal John Hancock on YouTube may not have a setup like mine. But I do remember him stating in one video his collection is double decked meaning he's got some games behind other games on his wall shelves.