Keep lavender on your short list for pretty flowering shrubs that are drought tolerant and can take southwestern summer heat. The roses have done a good job with little water, but they are due for a good soak.
The privet should probably not be on your planting list at all. Yes, they form nice thick hedges you can shear and bees love them, but they have become an invasive species in the west. After a little Googling I have decided to swear off privet. The USDA lists privet as invasive in Florida.
The Institute of Pacific Islands Forestry has several Ligustrum species listed as a threat on their Pacific Island Ecosystems at Risk (PIER) site. Glossy, Japanese and other privets are listed as invasive in Australia, New Zealand, Hawaii and the Western US Coast.
Perhaps a better alternative to privet shrubs for privacy would be a more drought tolerant, non-invasive and native Western Sumac. For evergreen versions that have similar leaves and growth habits try Lemonade Sumac (Rhus integrifolia), Laurel Sumac (Rhus laurina) or Sugarbush (Rhus ovata).
Thanks for dropping by and happy gardening!