IMO the cage you envision will be escape proof if the mesh is fastened to the PVC strongly enough.
How does this sound:
If you are using heavy metal mesh, the mesh will act as a diaphragm to keep the sides square, resisting being pushed out of shape when all the sides, floor, and roof are fastened together. If the cage is light enough for your igs to squeeze under the walls, you need a mesh or plywood floor.
Long ago I made an outside 8'X8' cube using 2X2 lumber for the skeleton, and very strong, very fine 1X1 tree netting to cover it. It's a very easy build. It was plenty strong enough for adult iguanas. It didn't easily push out of square. The only downside was that the iguanas spent all their time trying to bite through the mesh, and the net material was so thin that it bloodied their mouths so I had to abandon it. Now I realize the solution was to use much heavier fabric mesh that wouldn't injure them.
You can fasten horizontal 1x4's to the inside mesh walls to attach the shelves to. I would make 10 inch wide plywood ladders so the igs won't have to climb the mesh.