No longer have access to email for old account linked with steam.

I'm having the exact same problem... I contacted my old internet service provider to see if they could re-create my email account for a cost.  And they said no, the email service is now handled by a 3rd party - The Messaging Co.  I called The Messaging Co and they said they don't have the tooling to do it either.

So it seems I'm stuck... I'm in the queue to chat with EA Support again, but my hopes aren't very high.