grass is dormant

I moved into this house in Southern California a year ago.
The grass turns out to be zoyziagrass, which goes dormant in the winter, and stays short the rest of the year. Also, it doesn;t like shade.

I want to plant something else, like a tall fescue that will stay green yearround and grow in shade. How do I do this without ripping apart the current lawn. (i.e. less labor intensive) Can I just overseed? how about killing the current grass and overseeding.

Thanks in advance