Getting rid of the grass
Forget the pesticides! If you and your neighbors can tolerate it, use black plastic to kill the grass. You can even plant your drought tolerant plants while the black plastic is doing its job. It kills the grass and helps keep the moisture in the ground for the new plants. You can also leave the plastic and put rocks on top. Hopefully you won't change your mind about the rocks because it is a job to take them out. Start small and see if that is the way you want to go. Black plastic takes a year to kill the grass and invasive vines takes two years to die. And if you are lucky like I was, when I pulled the plastic up, globe mallow came up and filled it in. It was wonderful to see.