Make the nest cover to drop down on front of boxes. Even if planning on guttersThanks for the feedback!
There will be a hinged lid on the nesting box. I agree that a primary point of infiltration could be the gap where the lid meets the coop. I believe the overhang should drop water onto the angled lid which will then run down off of it. If that's not the case, I will install a flashing to protect that gap.