[daepp]

Im a concrete contractor but not an engineer (he said mournfully...)

Anyway, I don't know a building code/method in CA that would permit you adding the posts to the top of an existing slab.

The approved method would be to sawcut the slab, excavate down approx 12-15", and then fill with concrete creating what we call a pier. There are a large number of approved hardware pieces designed to be set it the wet mud at the top of the pier- they are galvanized and built to handle CA seismic loads and other forces (look up Simpson hardware).

That said, you do have options:

As we do new construction this doesn't come up much, but I've often wondered how big a diameter you could drill/core the concrete for a reasonable sum. For example, could you rent the tool/bit/saw necessary to do a 12" diameter cut? And if you only need a half dozen or so, it might be a pretty neat project.

Another option, like you suggested, is to simply have the roof extend a bit further and place your columns beyond your existing patio slab. There are probably dozens of ways you could make this look quite cool. The first that comes to mind to me is a red brick ribbon. You will be mixing mud anyways, why not create this final brick ribbon with mortar when your done pouring the piers for your posts?

Creative folks will probably give you better advice than I, but what you need can be done quite easily and without a lot of $$.