I set up my own domain, and forwarded emails from it to my Gmail account. Over a year and a half, every time I logged into something, I updated the email address to my own.

Eventually, when I jumped to FastMail, I repointed my domain name to it, and most of my new emails started coming over automatically, since the email address is now something I control. I monitored Gmail for a while regularly to catch straggler services. (I chose not to forward to avoid complacency with stuff going to Gmail before reaching my FastMail account.)