Most of the above will require almost as much water as did the lawn. You need to be looking for a very drought tolerant GC. And wire vine is just that..........a vine that can consume a great deal of real estate and grow to considerable height if anything available to grow up into.

I would look at baccharis (a CA native), dymondia, Ceanothus gloriosus or creeping thyme.

I applaud your interest in using a practical groundcover for your hot, sunny area. This spring, I bought some rupturewort and planted it in a dry, sunny area. I'm watching to see how quickly it spreads. So far, it seems to be performing well in the 90-plus temperatures we've been having here in Fort Collins, CO. If it looks viable, I may use it as a lawn replacement.

I've also been playing with Veronica pectinata because it's evergreen, has a beautiful green color and is drought-tolerant. It has been performing surprisingly well so far along the pavement at the edge of my front yard. Only thing is, after it blooms, it flops open for a while and looks ugly while it produces seed and recovers from blooming. But it's currently putting on more leaves and will look lovely again before long. So it's a question of whether you're willing to put up with a month or so of ugliness.

Creeping thyme is quite attractive. It can, however, die out and turn brown in the middle, making it unsightly.

Your mention of clover is intriguing. I researched it online. It appears that clover is quite drought-tolerant. But it's a short-lived perennial that needs to be reseeded every 2 or 3 years. A number of sources suggested combining it with grass. So if you wanted to experiment, you could seed Dutch white clover among your existing grass, you could see how it works out for you.

Did the below yard in northridge this last summer. The groundcover is dwarf elephant bush. Still growing in in the picture. It’s not perfect because it doesn’t really tolerate traffic but it’s green and from a distance it’s just a mass of green.. like lawn. U can always make paths of a lower walkable groundcover... a new one I have at a few residences that I haven’t taken pics of is ruschia lineolata stays to 3” I sometimes make puddles of walkable area and ornamental areas around.. or if u really need high traffic maybe use some synthetic lawn. The summers in San Fernando valley do get toasty.

Interesting plant, red berm. Reminds me a little of manzanita, from a distance.