Brad,
I have just gone through the slightly laborious process of removing the cloths, soaking in hot bleach & laundry soaped water, and finally a light scrub with a soft brush. Lather, rinse, repeat. The cloths have come out much cleaner, but still perhaps show a touch of aging...?
I'd post pictures but they are hanging dry now. I'll be using leftover glue from my speaker refoam job to re-adhere the cloth to wood. BTW, you cloths are in much nicer shape than mine...I found an old curtain at a Salvation Army last month, so I bought it to use as a new cloth, it looks great. However, the curtain was a bit too thick and it's now impossible to re-fit the grill, so I've gone through with the cleaning/scrubbing as of today.
Cheers,
THC