You can't do online migration, but migration via a snapshot should be quick and easy. Snapshots are incremental, so the best way to get low downtime is to create a snapshot, then when that one completes, unmount the old volume and snapshot again. The second snapshot should be really quick, especially if your application isn't write-heavy.

To add to the question, what happens with CloudFormation setup, where template doesn't specify EBS volume type. Will new instances use gp2 as default?