According to the cable company, the account does not exist. Somehow between the multiple mergers, it keeps getting migrated but is orphaned from their identity system.
(Although note that if you do this via Gmail it will leak your sending email address in the headers.)
Also, I think you might be able to retrieve the rest of your emails too. You might not have IMAP access, but at worst, you can write Google Scripts and have then upload your emails to another account. It will be rather slow but you should be able to copy all your emails this way. I don't think it should prompt you for a password when giving permission but I'm not sure; again, test this on your new account before trying. Make sure to wait like half an hour to make sure any internal password prompt timers expire.
I tried the gmail password retrieval system repeatedly, but could not get it to recognize me even though I had an archive of much of my email, so I thought I could be confident in answering questions about who I emailed and such.
So, I switched to a new email account. Luckily, I had a tablet that (to this day) is still logged into my lost gmail account, so I can tell that nobody I care about is still sending to the old address.
All in all, the consequences weren't that bad, although among them were the loss of my ability to have my straightforward [email protected] address...unfortunately using just my first initial and last name is not unique.
The concept of being able to reach a human being at Google is tantalizing but the fact is, I have such resentment and bile built up for the way things were designed that I'm not sure I want to reach out. And it doesn't matter a great deal anyway. I suspect in the long run it's lucky I learned not to trust them too much.