How about the project-based learning schools? They may not be considered "highly gifted" but "alternative" or "one of a kind" instead. Have you checked out those other categories on the LAUSD site? We are in the district for K and I see now that our neighborhood charter is an SAS school, but DD5's kindergarten class is not full of gifted kids...

My (perhaps overly optimistic) idea with project-based learning is that there is no limit for learning - you can take any subject to the hilt with self direction.

Here is the list, but surely you are familiar with this:

http://echoices.lausd.net/Mag/Default.aspx

and the school selection tool:

http://echoices.lausd.net/Magnet/programinfo.aspx