Is there any reason not to install a bathroom fan roof cap very near the edge of the roof, about 1.5 feet from the rain gutter? There is no soffit on this side of the house. Because of the location of the bathroom fan, the closest, most direct venting would be if the roof cap was near the edge of the gutter. I have a ranch style house, with gutter all the way around if that helps.
This is at the rear of the house, so aesthetics isn't an issue.