The speed brush is mainly for the wheel barrel areas. I have a lug nut brush, and a bigger brush for all the intricacies of the wheel face. I also have a dedicated wash mitt for cleaning all the wheel spokes, and a dedicated microfiber towel to get behind any tight areas, like behind the caliper. Except for the microfiber towel(until the 4BW comes), all of these get used when I clean my wheels.
One single tool will not cut it, unless you want to throw a strong acidic wheel cleaner and just blast it with a pressure washer. But you can ruin your wheels if you don't know what you're doing with this method.
Looking closer at your picture, looks like your brake calipers are getting pretty caked also. I also use the brushes on the calipers to keep them looking new.
You can always pull up a chair, turn on some music, and make it a better experience instead of bending over or kneeling on the ground and trying to get it done in 5 secs.