@F-14_Dave - Impressive problem, not in a good way. My sympathy.
How about backups of Evernote files or of old gmails? I’m assuming you are a Mac user. Do you have any Time Machine, Carbon Copy Cloner or Backblaze backups that might help? I’m not sure how you put the information into Evernote - did you use a text editor first, or just type directly into Evernote? Any temporary or work files that might have the information (backup code) you need?
Any backups of Google’s “All Mail” folder? Did Google send you the backup code by email? If so, maybe a backup of the All Mail folder might allow you to recover old emails without actually logging in to Gmail. Do you use the Mac’s Mail app to receive your Google emails? If so, maybe there is a backup of old email folders somewhere. In my iMac buried deeply in the Library-Mail- folder there are Gmail emails.