I'm not an expert, but I have vinca minor growing in a similarly shady spot and it's doing just fine thus far. I also have pachysandra in dry shade, but it stands up much taller than the vinca, which is mostly just creeping along the ground. I have seen areas that have more mature vinca cover and even when it's really thickly planted, it doesn't seem to stand up more than a few inches.

For very flat, I'd suggest Dymondia, although not at its best in heavy shade. Beach strawberry, Fragaria chiloensis, is another possibility for a very low growing plant. And although it does develop some height over time (it layers on top of itself), my favorite groundcover is Taiwan raspberry, Rubus pentalobus (syn. R. calycinoides).

All of these are highly rated as being very waterwise for SoCal gardens.

Thank you for the ideas.

Vinca minor works best for me. They come in various flower colors,

We are growing sedum reflexum 'blue spruce' in full shade, clay loam soil. Obviously it is not filling out as fast as the sedums we have in full sun, but it is doing quite well, with zero maintenance. No blooming yet, but s. reflexum flowers aren't that attractive, anyway.