I used to hang things up in the hallway, where there was enough wall space.
However, our "museum" had to have revolving exhibits.
You could decide with your son how long the work of art stays on the wall (a week? Two? Until the next one?). Then take some really good pictures of it before it is removed. Even real museums and galleries have to remove exhibits.
And your resident genius might be able to recycle some of the materials from, say, last month's project to use in one of September's creations. I hope he has a place in the basement or garage to store this basic material.
Keep the photographs of past projects in a scrapbook for you all to look at together, and perhaps he'll get ideas in the future from what he's done in the past.
Wow! A creative son! I'm so glad you're encouraging this. Maybe you want to take him on a short jaunt to an art museum some time, so he can see what other artists make and hang up on their walls.