I'm in the same boat, so I know the frustration you feel. I had much of the same information about my own grandmother (year of birth, state of birth, adoptive parents' names). The "breakthrough" for me was hiring a professional genealogist in the state of my grandmother's birth to unseal adoption records. If you're having trouble with the state department, consider the possibility that you have the wrong birth year. My grandmother's presumed birth date turned out to be the date her adoption was finalized. I was able to obtain her true birth certificate as well as her adoption paperwork. You may find that your best option is to research private adoption agencies in California in 1916 and making some phone calls...perhaps they're religious in nature and not government offices.

Good luck.