The best migration strategy to meet the requirement of minimizing database service interruption before the DNS cutover is to use AWS DMS to migrate data between the two Aurora DB clusters. AWS DMS can perform continuous replication of data with high availability and consolidate databases into a petabyte-scale data warehouse by streaming data to Amazon Redshift and Amazon S31. AWS DMS supports homogeneous migrations such as migrating from one Aurora MySQL DB cluster to another, as well as heterogeneous migrations between different database platforms2. AWS DMS also supports cross-account migrations, as long as the source and target databases are in the same AWS Region3.

The other options are not optimal for the following reasons:

Option A: Taking a snapshot of the existing Aurora database and restoring it in the new account would require a downtime during the snapshot and restore process, which could be significant for large databases. Moreover, any changes made to the source database after the snapshot would not be replicated to the target database, resulting in data inconsistency4.

Option C: Using AWS Backup to share an Aurora database backup from the existing AWS account to the new AWS account would have the same drawbacks as option A, as AWS Backup uses snapshots to create backups of Aurora databases.

Option D: Using AWS Application Migration Service to migrate data between the two Aurora DB clusters is not a valid option, as AWS Application Migration Service is designed to migrate applications, not databases, to AWS. AWS Application Migration Service can migrate applications from on-premises or other cloud environments to AWS, using agentless or agent-based methods.