Personally I wouldn't entrust my emails to a provider that I trust so little as to not abuse the trust of its users with their "Email import tool".
That is, if you even suspect that their "Email import tool" does shady things, I don't see how you can be comfortable with hosting your mail with them.
That said, you could use the google takeout function [0] to download your mail, and then upload via offlineimap of another similar tool. (I believe google takeout produces a .mbox).
Finally, I also host with fastmail, a great choice so far :)