Ideas on fixing shelf

I have an outside hanging table that I built originally for our PUP and then transferred to the TT. I went to TAP plastics hand had it made out of 1/2" thick High Density Polyethylene cutting board material. They can cut it to size, radius the corners and smooth the edges. It is lightly textured, so stuff doesn't slip as easily, is easy to clean and is totally water impervious. We normally use it for an outside dish washing station as I mounted in next to the outside shower.

I had a small folding table in the PUP that was made exactly as your de-laminated table. I replaced it with the same HDPE cutting board material, adding a marine grade plywood sub structure to mount the folding legs on. Worked great.