The reason I suggested the shelves is because they come in long lengths that could span from one end of the pen to another. Here's a photo of them. The 2nd photo shows the shorter pieces zip-tied together for when I was making my cage, but you would zip tie whole lengths together. People use them for lids on C&C guinea pig cages. The zip tie also can work as a hinge.
It's just an idea and you'd have to see if it could work safely.
It's just an idea and you'd have to see if it could work safely.