An update:
After contacting several more bike shops, most of which did not want to take on frame repair work, I found one that would—Harvest Cyclery in Brooklyn. When I brought the bike in, they were pretty confident they could straighten the frame out. I also asked them to remove pedals which were rusted and seized on when I got the bike, that I had been struggling to get off. Two days later they called and said both were done. When I got there it looked pretty straight! I also measured with calipers when I got it back home, and it is equal. And most importantly, I took it for a ride, and it rides straight now.
The guy I left the bike with, who was the one who performed the repair, was not working when I picked it up, so I didn't get to talk about the details of the operation. But from what I could gather from our original conversation, my string test might have been off, and assuming his first impression diagnosis was confirmed, he was going to bend the stays slightly.
Anyway, I'm pretty happy to have this bike on the road.