How can I retrieve my ssh passphrase from gnome-keyring?
After some searching and a bit of arguing, two small python programs turned up that do exactly what I needed. Both were able to dump all the passwords that are stored by gnome-keyring, including my ssh key's passphrase. (This is secure, of course, because it only works once I have unlocked my keyring.) See these blog posts for the code:
https://blog.schmichael.com/2008/10/30/listing-all-passwords-stored-in-gnome-keyring/
https://ins3cure.blogspot.fr/2012/07/extracting-gnome-keyring-credentials.html
Thank you, Michael Schurter and Liviu. I can now simply update my passphrase instead of going through the trouble of replacing my old ssh key on every system where it is installed.