To mount shelves, Trillium
screws the shelves to the wood window frames under the ensolite, that the windows
screw into. Where the front shelves end near the door, Trillium
uses wood blocks, glued to the fiberglass, under the ensolite. It should be possible to cut a smallish hole in the ensolite, carefully separate the ensolite from the fibreglass, then work a wood block under the ensolite. The shelf that you mount to the block should hide the cut made in the ensolite.
For a screen door, I would mount the frame to the closet on one side, and on the other side there is something like a pillar beside the door that it could mount to.