I gave this issue a lot of thought when I designed my coop. My solution was to put a piece of metal flashing above the coop lid, extending about 1/2 inch over the nest box lid gap. Then I used cabinet hinges whose throws allow the lid to come out and up and clear the flashing strip when the lid is opened. Also, I ran a strip of foam weather stripping along the gap to further prevent water/wind entry.
While this solution works, I would not necessarily recommend it, because it was a pain to construct. After all the work it has taken to build my coop, I've come to the conclusion that simple is usually better.
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While this solution works, I would not necessarily recommend it, because it was a pain to construct. After all the work it has taken to build my coop, I've come to the conclusion that simple is usually better.

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