The good news is Alameda County is not as bad as your neighbor to the south, Santa Clara County. Santa Clara County Sheriff Laurie Smith requires that a $20,000 "donation" be given when you apply for a CCW permit for it to be even considered. Your $20K is no guarantee you will be given one though. I have applied for one and I was rejected outright. (absolutely spotless record, many excellent references, legitimate and provable need for one, but no $20K check.)
Alameda County is considered to be a little (even a little bit is good) easier to get a CCW (Santa Clara is considered to be a "no issue" and Alameda is considered to be a "may issue"). You must be very careful in crafting your application. Make no mistakes, have excellent references, and don't screw it up. If you do you will not be considered again.
Good luck! And let us know what happens.