I sometimes suggest putting the gig bag inside a large contractor-type garbage bag or dry cleaning bag, which helps contain the humidity. With most gig bags, the zipper represents a large porous area, but the padding itself is mostly a barrier to moisture. Humidifying devices in my gig bags need to be refilled about 2-3 times as often as the same ones in hard cases.
My experience has also been that GA's fit into any dreadnought case. If there is a little extra room at the narrower waist, no problem.