It doesn't take that much more. Office 365's base plan is something like 35£/year, plus around 10£/year for a domain. They offer IMAP import so migrating from Gmail is seamless.
https://github.com/imapsync/imapsync
After cloning the repository and installing the listed dependencies (some Perl packages available in your Brew / Ubuntu repository already), you can do:
imapsync \
--host1 imap.old.com \
--user1 "old@email.com" \
--password1 xxxxxxxxxxxxx \
--ssl1 \
--host2 imap.new.com \
--user2 "new@email.com" \
--password2 yyyyyyyyyyyyy \
--ssl2 \
--errorsmax 1000000 \
--syncinternaldates \
--useheader 'Message-Id' \
--noreleasecheck \
--noexpunge \
--automap
Works great for importing to and from Gmail, but you might want to add a folder rewrite for the Sent folder (with --f1f2).But with FastMail, for those interested, the out of the box importing tools in their web interface work great, so no need for any command line tools.
It's a hugely flexible and versatile tool and it's quite zippy as well, can highly recommend.