How can I alter this high-protein brownie recipe?
Your goals here contradict each other. The reason that a brownie has a brownie-like texture is that it is made out of brownie batter. When you start leaving out some ingredients and pushing different ingredients into the batter, the texture of the resulting product changes. And when you add more protein, you end up with something that's drier than a brownie, because protein produces baked goods with a dry mouthfeel. 

To make the whole thing more brownie-like, you will have to add fat and some sugar. Flour is not needed, as it will increase the airiness. Maybe start by replacing the cocoa powder by dark chocolate which you melt over a water bath and add butter into it to melt. Also reduce the liquid (the almond milk - if you wish, add soy milk instead, it is the water content that is problematic here), and add more syrup, or better, dissolve some sugar in the liquid. Also, using powdered cream is likely to give you better results than powdered whey, and you won't need the chocolate flavoring from the whey mixture anyway when you are working with real chocolate. The mixture should be suitable for baking in the oven. 

Once you have gotten something reasonably brownie-like that way, you can try to start sneaking protein back in in increments, but pay attention to the texture. It will start going more in the direction of commercial protein bars with too much extra processed protein. You may get away with a bit more by adding more egg yolks, but do not increase the egg whites or you will get the texture further away from a brownie.