It was a whole subnet that was blacklisted. That said, they offered me a new IP from a couple different subnets as replacement, so I don't think it was too hard for them to do it. They would let me have an extra IP, but wouldn't let me run the two IPs concurrently for more than 24 hours.
This was especially frustrating since the subnet was blacklisted due to linode using generic PTR records by default. I needed a solution that didn't eat into my vacation time, so I ended up setting up a second server in the same datacenter and making it forward connections. That effectively got me a new IP for $20.
Just to be clear, I'm not complaining about it. I think they handled it fine. But I wouldn't hold them as some bastion of support perfection.