Quickest way I have found for the really hardened flat black ones is to take your favorite solvent, POG, or gel solve and apply it to the spot and then poke it full of holes. I like to use the Crane seam roller. They cost about 20 bucks but if you don't have one you can even use a fork to poke a bunch of holes in it.
Do this before before you even set up the cleaning equipment. By time you get to them during cleaning they will be soft and pliable and come out much easier.