Have you considered getting your own domain?

I have my own domain, but doing your own email is too hard. Can I use my domain email address with fastmail? Is it just a matter of setting up mx records? Will I be able to send/receive mail like normal without getting blocked by the big players?

Fastmail not only supports custom domains, they will handle your DNS as well, and they will automatically configure the MX records if you do that. Here are their docs about that: https://www.fastmail.com/help/receive/domains.html

In my experience: yes, yes, yes.

FWIW, it's not that big of a hassle: just set up email forwarding & have everything sent to your old gmail account sent to your new email, done.

Doesn't forwarding require going through the original provider? Can they still read the email? What if they shut down?

Sure, but you don't hand out your old email anymore, and really important things you can migrate as you see fit over time. I used to have a gmail address, and basically nobody uses it anymore (and if they do, it does get forwarded).