Quote:

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I vote for some of the adhesive backed foam insulation you use around window AC units on the bottom of the shutter and a bit on the door as well to form a nice seal. Cheap, tidy looking and effective.

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That might be tricky. The gap is wide on the left and right (4") and narrow in the middle (1.25").

Some photos:

Outside, with everything closed:


Outside, slot partially open: