Thanks for all the input, everyone. This idea came about because we are pre-approved to go to the mid-600s or even low 700s, but that felt risky because getting a house for $600k involves starting with a house priced in the $500s and bidding up. Many homes need work, and a $3000 per month mortgage plus $100k+ of renovations sounded terrible. There's no point in bidding on a home priced at $620k, because we have to pay $500 for a pre-inspection and sewer scope just to make an offer, and we will likely get outbid. We can save up for the next price point, but by that time the market may have risen another 10%.
Researching building has been enlightening and has helped inform our strategy. We are not ruling it out entirely. Unfortunately, building costs in Seattle are rising as quickly as house costs. A few years ago, one could build something nice for $200/square foot, but now wait times for contractors are long and the prices keep going up.
After some more thought, we might now wait for a small, nicer 800 sq foot cottage on a good lot in one of North Seattle's last 'affordable' neighborhoods, which we could hopefully get for $450-525k, which would be a much more reasonable mortgage of $1900-2300 per month. We'd build a detached studio for teaching, then maybe add on to the main house later. (Or, just have one child and never need to expand, although I really want two kids..) Irritatingly, many of these properties have no garage and zero closets.
Until now, we had been renting an 800 square foot cottage for cheap and it sounded foolish to buy effectively the same thing, pay $1000/month more for it, and take on the inevitable renovations. However, today our landlord raised the rent by a lot.
It's too bad that all the high-paying jobs are concentrating in the cities and driving the prices up like this. And, oh yes, I have fantasized about ditching this overpriced, traffic-ridden city and moving elsewhere, but our jobs are rewarding and we don't have the cash to be financially independent yet.