Engineering help needed

The whole thing (including the back) is made of veneered 3/4-inch MDF and has carpentry joints where the back/sides/top and bottom shelves meet.

If the 3 middle shelves had been attached to the back they wouldn't warp, but you also wouldn't be able to move them up and down. Aside from the shelves warping it's pretty rock solid and worth saving.

I got some L brackets, seems like a good way to go. Eventually I'd like to have floor to ceiling shelves built into the wall but that may be a few years down the road.