Pay more. Google and Facebook use ridiculous interviews because so many people want to work there. They still hire thousands of people every year. Why? Mostly because they pay mid-level engineers over $200k. Can't afford that? Then we're not talking about "not finding people" anymore, just about not affording them.
From talking to friends and family that live out there, plus a few folks who used to live in the Bay Area, someone earning $120k here would have to earn at least $200k out there to get the same standard of living.
So are people flocking to the DC area to work as software engineers, then? If so, good job. If not, you know what you have to do.
> to get the same standard of living.
That highly, highly depends on what you spend your money on.
People talk about salaries, they know who the top hitters are. Here in London there are many hedge funds you never heard of that have 20 engineers fighting for one spot, because they pay 100k GBP, whereas most startups complaining about lack of people pay 40k.