Can't change Adobe ID on Digital Editions

I am struggling to load a book onto my Kobo and the advised wisdom is to deauthorise and reauthorise your computer. However, my ADE is stuck using an old ID; I changed my email address with my Adobe Account, so the email address now doesn't work with the password, but the new email address hasn't transferred onto ADE.

I can't change my email address back to the one on ADE, because I can no longer access the old email address to verify the change. I have also uninstalled the programme and resintalled it, but it just automatically goes back to using the old email address. I spoke to the chat agents but they were no help, and said that they can't give technical support for ADE because it is a free application. 

Does anyone have any idea how I can change the Adobe ID associated with my ADE? My fear is that it's not possible, but I have manged to change my email address with every other application / company I use, and this is the only exception!