I seem to recall that El Toro zoysia is widely sold but maybe it has changed a lot in the past 5 years.

I did a quick google. Here's one that came up -

http://www.whittierfertilizer.com/sod.html

Why do you want zoysia? Are you having lawn troubles and you think zoysia is the solution? Are there pets or children involved in this project?

You have a golden opportunity that most people in the US don't have. Go visit both Huntington Library AND Descanso Gardens to see the grasses they use. Because you have shade, you should look especially at the St Augustine as well as the zoysia. There are only a few varieties of zoysia that can stand less than full sun all day.

Zoysia is fine bladed while St Augustine is coarse. You have to be ready for that major difference. Zoysia should be mowed low while St Aug should be mowed at the mower's highest setting. They may not do that at your local garden destinations. When you mow it high, St Aug is much easier to live with than anything I've tried. In my San Antonio neighborhood there is always someone trying to make zoysia work. Usually they only last half of one season before they switch back to St Aug.

So a search on "funkyamazon st augustine" both on this forum and on Google. She is a GW member and member of another lawn forum. She is also a neighbor of yours in Pasadena (near Cal Tech) who has turned her St Augustine lawn around during the last few month. Going into the summer she hated it and now she has torn out a new installation of Kentucky bluegrass in the back to replace it with St Aug. If nothing else she knows where to buy grass in your area.