You say ring of crud, what color is the crud? Is it in the recessed areas of the wheel that have a texture or is it white and flakey looking?
Reason why I asked. These wheels are clear coated and they will over time start to lose the clear coat. That can make them look chalky in certain areas. Most of the time this can be from neglect or someone using some really harsh chemicals in the past.
If they are rusty brown in the areas of the recesses, then you can get some Sonax Full effect, Iron Out, or another that is specifically formulated to break down the old brake dust and iron deposits. I have also taken light steel wool and agitated these areas. It could take more than a couple of times to really get them cleaned.
HUMP