I'd like to try Erin McDowell's "Cakey Brownies" recipe from "The Fearless Baker", but the volume and weight measurements for the flour do not mat...

That's the trouble with comparing weight and volume measurements. There just isn't one standard weight that everyone recognizes and accepts. Even among the experts there is a difference of opinion as to what 1 cup of flour will weigh. As a result you have a range of weights used by different bakers. I personally prefer to bake by weight, so I use whichever is listed in the recipe because that is what that particular baker is using. For my own personal conversion, I use 120 grams as a starting point for a cup of flour. I find it best to start with the lesser amount and add by the spoonful as needed to achieve the right consistency to produce the texture brownie you are looking for. Flour moisture content can vary, if the day is dry or humid, so absolute weight measures can't really be written in stone.