Reddit reviews Aluminum and Nylon Door 11/32" Bristle Weatherstrip - 72 in long
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Flexible Bristles Allow a Seal on Even and Uneven Surfaces
I don't know how well this would work but maybe you could fasten bristle weatherstrip to the outside perimeter of the doors. You could paint the frame of the bristle strip to match the door. That would eliminate having to mount stuff directly to your walls and probably be a much cleaner look.
https://www.amazon.com/Aluminum-Nylon-Door-Bristle-Weatherstrip/dp/B00QL4L3Z0