>Is the west coast (Seattle) really this much more expensive?

In a word, yes. Seattle is one of the most expensive areas in the country.

>We want to live on $4k/mo including rent, which we’d like to cap at $2500/mo.

Are you both homebodies (or free outdoor-recreation bodies)? No drinks with friends, no dining out, no weekend getaways each month? If yes to the first and no to the second, you can probably do it on $4k…but it will probably be closer to tolerable than comfortable.