I've moved to my new Linode. It turned out to be even easier than I had anticipated: Linode has a feature that lets you swap your Linodes' IP addresses! I ended up needing to reboot both Linodes, and I had some SMTP configuration issues on the new server (I could receive email but not send it), but now that I got that sorted out, things are going pretty smoothly. Do note, though, that CGI currently does not work, so some aspects of my blog are broken. I will fix that shortly.