Which migration strategy will meet this requirement?

Explanations:

Taking a snapshot of the existing Aurora database and sharing it with the new AWS account allows for a straightforward migration process. The new Aurora DB cluster can be created from the shared snapshot, minimizing downtime since the snapshot captures the database state at a specific point in time. However, the data is only current up to the time the snapshot was taken, so there would be some data lag until the final cutover.

Using AWS Database Migration Service (AWS DMS) allows for continuous data replication between the existing Aurora DB cluster and the new one created in the new AWS account. This method supports minimal downtime since data can be migrated incrementally while the source database remains operational. When the data is synchronized, a final cutover can be made, which minimizes service interruption.

While AWS Backup can be used to create and manage backups, it does not support sharing backups directly between accounts in the same way that snapshots can be shared. Moreover, even if a backup is shared, restoring it would not be as efficient as using a snapshot for Aurora databases, leading to potential downtime.

AWS Application Migration Service is primarily designed for migrating applications and servers, not for migrating database instances like Aurora MySQL. This option does not provide a suitable solution for database migration and may lead to increased downtime or service interruption, which does not meet the requirement for minimizing interruption during the DNS cutover.