That really sucks

When I stored my PNY $1's in a 500ct. "mahogany" case I was always concerned that they might absorb the wood stain since it didn't appear to have a coat of lacquer. It never happened, but it appears that my fears weren't misplaced.
For cleaning white clay casino chips, I've always had great success adding two table spoons of laundry detergent to a 1-gallon bowl filled with warm water. Throw in a half scoop of OxyClean and let them soak for 15-20 minutes. Brush 'em off with a toothbrush, put in them in a bowl of clean water, and towel dry them. This method works on all white Paulson casino chips and also worked on my BCC Samurai Palace chips - so I think it will be safe with the BCC clay mixture.
Although I can't explain the science behind it, I once wrapped up a stack of clay chips in a dryer sheet to try and eliminate the cigar(ette) smell and it worked quite well to "suck out" the smell. Perhaps it's worth trying something like this that will absorb rather than scrub off. Regardless, it didn't damage the chips and left them smelling laundry fresh!
Hope this helps. Good luck cleaning those fantastic custom BCC chips!