My vent solution is here:
One thing to note: when a sliding window is open, even if you seal the opening, there is another gap on the other side of the sliding window, between the frame and the glass of the non-sliding window. My build closes that with an additional piece of foam.
Also, since taking those pictures, I added weatherstripping to the sides of the foam insert. We’ve been having some sub-freezing temps here in Seattle the past weeks. With the blast gate closed there hasn’t been any problems with leaving it installed. (Just always remember to open the blast gate 