I have little doubt that the Adam's Eco Wheel Cleaner will take care of the brake dust. I have used it on wheels that had not been cleaned in over 40 years and it worked. However, there are a couple of additional methods if you need something to soak in for a few minutes and that is white vinegar and baking soda one one more if you need something more aggressive. The white vinegar and baking soda can leave what appears to be water spots if you let it dry and it can result in an uneven look, but it will polish out with a little effort.
According to how bad they actually are, I would recommend going with compressed air to get as much off as possible while in a dry state, next is the pressure washer then Adam's Eco Wheel Cleaner first and then white vinegar and baking soda if needed and last is #0000 steel wool, the same as you use on your windshield.
Again, the white vinegar and baking soda or #0000 steel wool can leave marring that will require extra effort to get them looking proper again.
Corrected: I had to look at my notes following @falcaineer statement about staining with regular wheel cleaner. After checking my notes, I use Eco Wheel Cleaner and have updated this post accordingly. Thanks for catching that Chris.