There are stronger chemical wheel cleaner out there but they tend to be acid based and I generally stay clear from all of them.
I had the same issue on my wheel. I managed to resolve it by using the following.
2 applications of CarPro Trix (Iron & Tar Remover)
Meg D140 Wheel Brightener
Unfortunately, both Trix and D140 require some brush work so it is not a simple spray on/ spray off. Be warn.....both Iron X and Trix have a terrible smell and gloves are highly recommended when dealing with them. A well ventilated work area is a must.
After Claying, I applied 2 coats of BlackFire Metal sealant ( Paint Sealant works just as well but I have the Metal Sealant in my tool box so I used it). The sealant doesn't stop the brake dust from forming on your wheels but it does makes the wheels so much easier to clean. Now-a-days, I just knock them all off with water without the need of a wheel cleaner.
If you are serious about getting rid of all the nasty stuff on your wheel, I recommend you take the wheels off and clean them one at a time. It is actually much easier this way instead of bending over at some funny angle trying to get at them. This would also give you the perfect opportunity to clean the barrel.....while you are at it.
What is absolute control???? Having the means and the abilities to exercise it at will but....chooses not to.