First, others may have had similar poor experiences at the same property but won't know unless you provide the property's name. Perhaps someone else here can help you out, but never will. Nothing to protect by not naming the place.

Second do you know how the property's insurance company came up with $1,000? Just because the insurer is offering $1K, doesn't mean that the property isn't on the hook for more. But, I presume that the insurer wants you to release the property in return for the $1K.

Third, as others note, start checking your own insurance policies. Homeowners, credit cards used for the travel (although this is sticky because you may not have checked in). It may be easier to make this claim against one of those and let them slug it out. It may also be easier to simply claim against the property. If it really is a 5* (are there really any in SF?) it ought to be able to pay a $12K claim.

Having said all of this, you may have a mess on your hands. You may want to check California law on liability here. It may limit the "innkeeper's" liability and if it does you may be SOL.

To be fair, whether a bag is locked in a room accessed by a bunch of bellmen or in an employee's-only hallway, I can't conceive of leaving $12K worth of items including medication and jewelry. That kind of stuff stays with me no matter what.