> It would require systematically changing my email at the 300+ sites I’m aware of

Yes, this can seem overwhelming. That's where the auto-forward helps. This is what I did: initially changed emails at the big ones - banks, govt, etc., maybe 10 or so. For the rest, when an email would come in, I would change it for just that one. It distributes the workload over time and is much more manageable.

> I tied to change my email 13 years ago. My own mother still sends to my old gmail account

This is where the reply-to setting becomes important - most email clients will use the reply-to when responding. For persistent ones, go into, say Mom's contacts, and update the email there, deleting the old one. Had to do this with my parents and family. Don't make them do it, do it yourself.

How to set reply-to: go to Settings > Accounts and Import, click "edit info" next to your email address in the "Send mail as" section, select "Specify a different 'reply-to' address" in the pop-up and enter the desired email.