Texas A&M recommends expanded shale for aerating clay soils, but I don't know how much that would cost in bulk. Probably a lot. :/
One option for lowering your costs / efforts would be to alternate amended areas with areas filled with clay-friendly plants. Zone 10 is sometimes considered to be the start of the tropics, so we here in the subtropics have some choices with a fairly tropical feel.
For full sun, maybe consider:
Crinum lilies
Agapanthus
Some native hibiscuses (kostelezkya virginica, hibiscus laevis)
Daylilies
Baptisias (baptisia alba, baptisia australis, baptisia australis minor, baptisia bracteata)
Chile pequin (a native pepper that I hear is very hot)
Turk's cap
For part shade, maybe
Sabal minor (our only native palm, I believe)
Sago palm
Canna lilies
Althea
Daturas & brugmansias (if you have no small children or particularly adventurous teens around; they're hallucinogenic)
Chile pequin
Turk's cap
Ginger lily / butterfly lily
Spider lilies (hymenocallis)
Passionflower (passiflora incarnata or passiflora foetida are natives)
(Multiple edits to get rid of extra "help" from autocorrect).
