I would not go with the PVC. Its a small roof so I would probably make a roof frame out of 2x2 lumber that sits right on top, then hinge the whole thing from the bottom, on the high side. Install corrugated roof panels on top, perhaps using 6ft panels (based on 12ft cut in half) so you have nice overhangs, the overhang on the hinged side would help keep the "lid" from flipping all the way 180degrees, which will help when you close it again. May need to space it away from the coop itself a tad, so I'd just disconnect the run and add in wood spacer, like a 2x4 which will give an extra 3.5" gap. Probably only take 10-15 sticks of 2x2 to do this and a few hours and beers to assemble it. Hope this all makes sense, does in my mind