Have you looked in places outside of the traditional NYC/SV/Seattle area? Not sure where you are located, but it might be worthwhile to look around for talent where nobody is looking.
The other side of that is that tech companies based outside the NYC/SV/Seattle area don't get funded at NYC/SV/Seattle-style valuations. (likely because those cities are where the tech company investors are). And to start a tech company, you do need your company to be based where your developers are.
While I understand remote workers participate less in building the corporate culture, there is no reason you can't have talented developers work for you and supplement your team if you expand your hiring scope to include freelancers or remote workers.
We look all over the country, but Netflix (where I work and hire for) doesn't really do remote employees, so we ask them to move to Los Gatos. Unfortunately this means we are looking at people who are already willing to move.
That might be the crux of your problem (and the problems a lot of other companies are having with hiring). This is just my totally biased outside perspective, but it's easy to get remote work right now. Why in the world would I ever want to move to California?
I'm seeing this become an issue a lot with companies that need good development talent but just don't understand that it might not be something they can find locally. Good developers can (at least right now) live wherever they want in the country and make plenty of money. Apologies to anyone living in, say, Wichita, but why would I move there* if I didn't have to? By forcing your development teams to be local, you're limiting your talent pool or you're picking up C-grade developers from other places who are desperate for a job.
I'm sure you're also facing some problems finding folks to move due to the high cost of living in Northern California.
I've been open to moving out there for jobs, but based on what I've seen, the salaries aren't high enough to offset the tremendous cost of housing. Especially for those who come with families and school age children.
I just took a quick look at the engineering page at jobs.netflix.com and over 3/4 of the postings have "senior" in the title.
Maybe you should focus a little less on finding people who have already done the job you think you're looking for and focus a little more on finding smart people who can develop into the people who can do the job you haven't thought of yet?
That is unfortunate. Could you have part of your team move out of Los Gatos to another area? Or perhaps set up a remote office in a secondary city for people to gather at? I know Facebook has one in Austin and I could bet it had to do with the talent crunch.