River birches in a drought area will be hard to maintain but your Zelkova is drought tolerant, so it won't need much water. You can attain an Asian garden look with native plants or low water use plants. The picture is from Greg Rubin's website and the article is from a Japanese/American newspaper.

Ofdm, I think you are asking that design advice happen in a vacuum. While it's GREAT to see a plan, there is no context for its surroundings. In conjunction with it I think you should provide a photo of the space where the house is in the background and we can see from lot line to lot line. That would help a lot.

Thanks all. Here is a picture of how it looks right now:

Woodland ....? That's going to be hard to achieve without a multiplicity of tree trunks. And starting with a Zelkova, I think you have room for one more. If you wanted to have a lot of trunks combining into a single canopy that would look fine but I think I would start with a smaller tree (mature 25' to 30') and then have a group of a half dozen across the front portion of the lawn. And start them all at the same time so they don't have a battle with a lot of maimed & wounded.

I wouldn't have any grass, but groundcover instead ... whatever would work in your climate. I don't know what you would use for shrubs and perennials but I would keep it simple. A Jap. maple shrub form could go in front of the right end of porch, not crowding it too tightly. A tree form could go at the left side near the walk. I would widen the walk to front porch, especially if using groundcover. Even with a tightly clipped lawn, it's too narrow. A massive boulder might work as additional interest somewhere in the lawn area. I doubt I captured the flavor you're looking for, but hopefully it's a brainstorm that will lead you to the next stepping stone. (Scale between picture and plan is out of whack. Make the best of it.)

If you have time to visit both Descanso gardens and the Japanese garden at the water reclamation plant in San Fernando http://suihoen.thejapanesegarden.com/new/. Those are good examples of Japanese gardens made out of open spaces. The Descano garden is shaded with large trees and the San Fernando one has large open spaces that have sun but still have the rolling hills and boulder aspect of the japanese garden style.

If you want it shaded there are suppliers of very large trees I can refer you to or you could wait for items to grow in.

If you are interested in a design I do design in the south bay area and can meet discuss options of what you could. Feel free to preview my profile and let me know if you would like to discuss.