My coop was built spring 2013 and the external nest box lid edges started separating from rain within the first few weeks after building. We cut a larger piece of siding board to allow overhang on the exposed 2 sides of the lid, painted it with a water repellant stain and glued onto original lid with liquid nails. It has held up quite well. And I brushed liquid nails along edges of the original plywood lid edges to prevent further issues.
Could you consider just attaching a water repellant cover to the one you have. If not, I think you need to add something to keep inside nests dark.
You may be more experienced with plexiglass than me and DH were. We bought large sheets of it last winter and attached to the windy side of our coop/run. It was difficult to cut, splits easily. Drilled holes for screws,and many of those split as well. If you decide to use plexiglass, try to find it in the size you want. Probably should frame it so you won't get leaks at hinges?