I live in the PNW....nothing is sadder than a bunch of wet hens! Why not split the difference and roof the two panels closest to the coop to allow a little more freedom during rain, and wire over the last bit closest to the door. I always felt so bad when my girls had to hover under the coop...
This is a little thing, but I would try turning your nesting crate on its side so the hen feels more secure with a "roof" over her head. Might not work, but cheap and easy to try.
I lost several to fly strike and being egg bound. I have had an eagle unsuccessfully swoop on my free range girls. Hand fed a cross beak that lasted about 6 months. Recently had something eat one of my girls, but not sure if it was a natural death with canabalism or an actual predator. I don't...