How can I change a defunct Apple ID email address?

Perhaps you could try addressing the problem from the other side of the issue. When I faced a similar problem with my now defunct student email address on another account, the solution turned out to be contacting the IT department of my old school and convincing them to temporarily re-instate my student email address. Once I convinced them to do it, it turned out to be a really simple process. I was able to change over and recover passwords from several services tied to the old email address, and once completed just had them deactivate it again. Your milage may vary depending on your educational institution, but it's definitely worth a shot.

Try to use https://appleid.apple.com/ which allows you to change Apple ID details:

Select "Manage your account" and use your existing Apple ID and password to log in.

Choose the option to edit your Apple ID/Primary Email Address:

and enter a new one.