[gonvaled]

Your solution is (was?) to use your own email address (with your own domain) with email forwarding to your gmail address. This way you do not make your gmail address public, and can move frontends easily.

This does not solve the fact that your email archive is in gmail though.

[reificator]

I would assume that your archived emails would be available for download via IMAP. Is that not the case?

[sneak]

Not if your account is locked. You need to back them up periodically manually while you still can.

The program to do this is called offlineimap.