As mentioned in my article (referenced in first post), the Twenty One grille "cloth" is plastic, not really fabric. I cleaned mine with a soft children's toothbrush and diluted Goof-Off. You could probably use any mild cleanser. See the article for more details.
Not so easy for the earlier Model Eight. I'm working on one of those right now. The fabric grille cloth is stained and difficult to work with. It's glued to the solid Masonite speaker board, so removal doesn't look possible. Cleaning in place might work in theory, but many fabrics shrink after wetting. We'll see . . . .
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html