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Take photos, then discard.
I have reviewed the school stuffs that my kids have accumulated through the years and perhaps the bulk of them are books but a large portion is made up of those nice and sentimental preschool artworks. Surely, you want to keep them so your kids can someday go back and tearfully remember those early years. If you cannot find a space to properly store them, why not just take photos of them and store them in the cloud? Capture them before the colors fade, the pages torn. Create a collage out of them and print out, put in frames to hang on your wall. You may keep the best and most precious if you want but the idea is to discard majority of them once they have been photographed.