Have you considered Ice Plant?

Or any other locally adapted groundcover. Some varieties of ice plant are considered invasive, especially in California.

We are in California. So let me check if ice plants can survive here.

We put rock mulch on a steeper but shorter slope than that and it hasn't budged. You would need sharp edged instead of rounded edges so it locks in place.

Prostrate acacia is a low water user that looks great on slopes and Myoporum parvifolium is a lower and greener plant that also makes a great low water use ground cover.

Buy groundcovers, mulch them until they grow in. As the mulch drifts down and breaks down, the groundcovers should spread. There are often nurseries that cater to pros which sell an entire tray (usually 50 plants) of plugs retail. This can be a good way to get lots of plants.

If you want a groundcover to cover a huge area like that, might consider just covering with seed and watering lightly for a couple of weeks. Many grow easily from seed. Ice Plant for example. It would be far cheaper and easier. You would also have a much wider variety of cultivars to choose from.