Theres obviously a few ways to go about it. Going w/ a stronger cleaner is certainly one way to do it, but remember, the stronger the product, the greater chance of it harming some types of wheel finishes. For instance, Meguiars makes a hot wheel cleaner, which, on uncoated surfaces can actually harm the finish if the product isnt neutralized prior to rinsing it off. I'm not saying that will happen to an oem/clearcoated finish, but I do want you to be aware of what some cleaners can do to a wheel.
With that said, the next step up from your p21s wheel cleaner would be the p21s wheel gel. You can spray it on, allow it to dwell and agitate w/ a brush prior to rinsing. Chemical Guys also developed a citrus based wheel gel which is quite similar.
If you wanted to go even a little stronger, Poorboys Spray n Rinse is pretty strong stuff and I've used it on a lot of wheels w/ caked on brake dust to help remove it.
One other option for you is to use some clay. A stronger cut of clay can help remove brake dust. In fact, on really bad wheels, I have had great success using spray n rinse, a heavy cut clay and poorboys ssr2.5 polish. I'm not saying your wheels are bad enough to require it, but wanted you to know how I've gone about cleaning up really bad areas.
I also think that the brake dust being in the corners will make it a little more challenging than if it were to just be on the inner barrels, b/c the area you're working with limits your use of tools and ability to apply good pressure across the area.
Anyway, here is a link for you to check out some wheel cleaners. Wheel Sealants and Wheel Cleaners
And as Spencer mentioned, you might consider going w/ a wheel sealant to help future cleanings. Poorboys Wheel Sealant is a fabulous example of this type of product, however, dont feel limited to products marketed as just "wheel waxes or wheel sealants". I apply Optimums OptiSeal
to my oem M3 wheels and it works beautifully and really cuts down on time due to its design.