Paving stones driveway base Wrong or Right
Go to the Interlocking Concrete Pving institute site (icpa.org) for installation and material specs. Make sure you are considering interlocking concrete pavers instead of the unknown "steeping stones" that have dimension greater than 11" or so.
You certainly have soil problems in LA after seeing what I did for 6 months after Katrina. It was not unusual to run into a home (slab on piling) where for several years before the storm they sent the kid under the slab to run the cable for TV. Everything there seems to go down in time.
You are right - clay is rarely a good base even if it looks good and seems to "pack" nice.
A concrete driveway will have the same settlement problems, but cannot be picked up and reset because of the unstable sub-base.