So, I knew I wanted to use my own email domain going forwards to prevent this problem in the future. I got inbox@firstlastname.com set up, and forwarded it to Gmail. Then for about a year and a half, anytime I looked at account settings anywhere I'd change it from my Gmail address to my own address. (But it all still ended up in the same inbox.)
When I decided to switch to FastMail in 2016, I repointed that address at FastMail and the vast majority of stuff moved with me... instantly. FastMail also has tools to import your mail archive using IMAP for what's already in your Gmail account.
Now that all of my mail uses my own domain name, if I ever needed to leave FastMail, it'd be painless... none of my mail is going to a FastMail address to begin with.
My strong recommendation is that people do this even if they intend to stick with Gmail for the time being, just to give themselves the future option.
