In our house, they start out in the living room, then move to the kids' rooms, then to the garage if destined for the trash or to the attic if going into the "memory box."  Sometimes we stage things into the garage if we need to clear out clutter for a party.  Once something is in the garage, the next step is the trash can.  So throwing a party has secondary benefits.

Ideally, you would do something that would result in your kids making the decision for themselves to ditch the old projects.  Just what form that would take for you and your kids, I can't say.  Second best would be to have a frank conversation about how the clutter makes you feel (unhappy) and then jointly make a plan for getting rid of the projects, with a schedule like, "we will keep them until summer vacation starts."

You might even try bargaining, like, "if we clear out the old projects, we can get a new puppy."  Or something like that; maybe not a puppy.

Along the way, take lots of pictures of them (you probably alreay have) and put prints into the memory boxes.

But, ultimately, Mom and Dad need to make the household policy concerning keeping old projects, and enforce it objectively.