At the sake of being complicated, nothing compares to a chin comb, they have pointy tips which allow you to go through the fur without pulling live fur. I've personally never had luck with any other comb type, even a greyhound comb which some ranchers use for rough grooming.
$30 for a comb is nothing compared to having a dog groomed at a groomer. I do believe that Jordan had some cheaper plastic combs for sale in the classified as well, but not sure if he still has any or not. If you have 20 chins, that's less than $2 per chin. It's not just about making them look better, it's about them feeling better and getting better dust bathes by getting the dead fur out.