Mongomirror allows you to migrate particular databases or collections using the --includeDB and --includeNamespace parameters:

https://docs.atlas.mongodb.com/reference/mongomirror/#cmdoption-includedb
https://docs.atlas.mongodb.com/reference/mongomirror/#cmdoption-includenamespace

It would be helpful if Live Migrate allowed for use of these options as well to migrate subsets of data, instead of only migrating an entire cluster.