I have the same problem, but on the ZCP silver wheels. What I do is skip the wheels when I'm cleaning the car. because no matter what you're going to get some water on the rotors when washing the car and that will cause it to flash rust. Once you step on the brakes the flash rust will rub off and dirty up the barrel like how you have it in your pictures.
So I skip the wheels and clean them later on in the day after I've driven the car. When I clean the wheels, do not use water, do not use any product. Take a spatula or any sturdy stick and wrap a microfiber towel around it. use it to wipe the barrels dry on all 4 wheels. hop in your car and move forward about 4 feet. get out and wipe the barrels with a dry MF towel. hop back in your car move forward another 4 feet, repeat on all wheels. by then your barrels should be brand spanking clean.
PS: I had my 4 wheels opticoated.
My method is not perfect but I hope it gives you an idea on how to solve this problem. If money were no object, I think I would get another set of ZCP wheels/tires, and instead, I would just switch between the two sets of wheels every few weeks and clean the dirty set on my work bench. It's much easier and less stress on your back than crawling down on your knees and poking the rims with a stick.