After years of migrating my sites from one host to another, I finally landed with SiteGround. Although I now host some of my sites on a VPS through Digital Ocean, SiteGround is still my go to web host – highly recommended. They offer an excellent service with reliability, affordability, familiarity, and quality support. It seems they have also been working in recent years to meet needs specific to WordPress.
SiteGround Migrator aims to ease migration of your site to SiteGround services. I've not yet been able to give this one a test run. I reached out to support today and they informed me that, though the plugin itself has been released to the WP plugin directory, they are still finalizing development to ensure the service runs well. This could prove to be a very slick tool and I expect they will announce its release soon.
Thanks to Stanimir Stoyanov and Hristo Pandjarov for pulling this together!