Ask Mr. Smarty Plants

For openers, the plants you are using now are not native to North America. Since our expertise only extends to plants native not only to North America but to the area in which the plants are being grown, we cannot recommend either. Urticaceae solerolia, Baby's Tears, is native to the Northern Meditteranean, around Italy. It is often grown indoors as a houseplant, prefers shade and moderate moisture. It is considered a common weed in many places, and can be very invasive, almost impossible to control. We don't like invasives, either. Zoysia japonica, Korean lawn grass, was introduced into the U.S. in 1895 from the Manchurian Province of China.

Finding a native groundcover that will suit your purposes and the varying environments for plants in your patio is difficult.  Las Pilitas Nursery, which specializes in California native plants, has a location in San Diego County, where you are, and could probably help you more than we could. We looked at their page on groundcovers under 1' tall, but most of them seemed too tall to work in your situation. However, if you contact them or visit, they can probably find something that works for you.

We went to our Native Plant Database, looking at some of the very low-growing plants we have had experience with before that could work in your situation. A few of these were on the Las Pilitas list, and all are native to California. We also checked each of our selections with the USDA Plant Profile on that plant to determine if it grew in or near San Diego County. None of the five fit all your specifications. You are doing the right thing to keep the spaces between your flagstones permeable; that is, permitting water to go down into the soil for tree roots that may be trying to survive, but you  could find that putting pea gravel or a good quality shredded hardwood mulch into those spaces will accomplish the same purposes without the maintenance.

Low groundcovers for patio in San Diego Co., California:

Symphoricarpos mollis (creeping snowberry) - part sun to shade, low water use

Phyla nodiflora (turkey tangle fogfruit) - semi-evergreen, perennial, sun or part shade

Fragaria vesca (woodland strawberry) - part shade, shade

Heuchera rubescens (pink alumroot) - perennial, part shade

Heuchera rubescens var. versicolor (pink alumroot) - perennial, shade Pictures from Google

From our Native Plant Image Gallery:

Symphoricarpos mollis

Phyla nodiflora

Fragaria vesca

Heuchera rubescens