Is the mesh fabric or metal?
I am no expert, but have used pure ethyl alcohol to remove that gooey foam rot. However, it can also remove some paint and lettering. I have no idea if that AKG item can handle that or not.
Also, I'd want to try removing the outer grille housing from the diaphram assembly to clean it. This may not be practical without special tools and training. The mesh is especially problematic. External cleaning with fluids could dribble onto the diaphram unless you remove it. Even careful wiping, plucking and Q-tips on the outside could be risky, depending on the chemicals. But you may be stuck with that.
I think someone could easily spend 4+ hours on each capsule doing this kind of cleaning. $95 a capsule might be worth it, if they'll get them completely clean and undamaged.
I feel for you, I've also had some foam rot problems. PSA: everyone look through your polyurethane foam cases AND windscreens for foam rot. I think it can happen at any time after a few years, depending on the foam manufacturing. When it starts losing springiness and gets a bit tacky, time to toss it and replace it. (The stiffer polyethylene foam seems more stable)