You could clean it as you would wool carpet. Know that the silk will shrink and curl and that you'll have to hand-groom every bit of it with steamer and brush to bring it back up. Charge accordingly, they have a huge investment in their carpet.
You could dry solvent clean it and avoid the grooming hassle, but you're going to use a lot of solvent.
Or, find someone that will lend you a rotary DriMaster.
That carpet would look good in your living room. You could put the stain magic spot under your couch (the couch with the bleach spot) and nobody would know but your accountant.