How to migrate some databases sources from a directory active to another

I need to migrate two SQL databases from a subscription located in one Azure Active Directory (tenant) to another directory (tenant). The databases are live, receiving incoming data. I initially attempted to use Azure Database Migration Service (DMS) and Azure Data Factory, but they have limitations when it comes to migrating between different tenants.

I am seeking confirmation on which service is best suited for handling this cross-tenant migration while maintaining application availability and data integrity during the process. Managing downtime and ensuring continuous data synchronization is critical due to the active nature of the databases.