One other cleaning method that might work and uses NO CHEMICALS would be steam cleaning. I own a McCulloch steam cleaner (see this Amazon Link) and I have used steam cleaning to kill and remove minor mold and mildew in some DIY cleaning projects (works great for cleaning my BBQ and outdoor kitchen tile without using harsh chemicals). The only caveat is that it takes A LOT of elbow grease to scrub and clean away heavy deposits. The steam really helps loosen it all up, but you still have to scrub it away. Sometimes you can rent steam cleaning systems from local hardware or rental stores. I bought mine because I use it a lot.

Hope that helps.