Great news, Eric! I enjoyed following this thread and am glad you made your own success.
This suggestion is a day late and a dollar short for you this time, but I'll throw it out there for future use or for someone else who's in a similar situation in the Bay Area. I'm recently retired as a rep for a major carpet mill, and I covered most of the Bay Area for about a dozen years, calling on all types of carpet and flooring stores. Many of the owners and salespeople have rentals themselves. They also cultivate property managers and individuals who own rentals. They know when properties are going to be available because they get the flooring jobs before the properties are listed. Sidenote: At one of my old accounts, the carpet showroom was actually kind of a side business. The owner (a former pro football player) had the retail operation, plus he owns over 500 Bay Area rental homes. Runs them both out of the same building. Smart dude.
I'd print up a generic rental application form (I don't have to tell you not to fill in the credit details-put "available asap"or somesuch.) and write a cover letter. Bonus points if you put a picture in the letter in which you (and your family, if applicable) look neat, tidy, quiet and above all, trust-and-credit-worthy, lol. (Crazy isn't it? They don't provide photos but you have to.)
Then, I'd search out every flooring store and carpet installer in your desired area. Go in and talk to them; you'd be surprised at who and what they know. Make sure they are not with a customer or you'll just piss them off, because they are not busy most of the time. Think weekday mornings if your schedule is flexible. Take their card, give them several of yours plus your info and ask them to keep you in mind if they hear of anything. If you make a good impression, you'll hear something from one of them. Circle back around occasionally until you find something to let them know you're still interested. Out of the box thinking, and a little extra effort, but it could be a big payoff if you can get there before their ad ever gets placed.