SQL Server on Windows Server (VMware) - online storage swap
Follow the process here: Move Database Files to move the databases to the new storage.  You can leave the insance online, but each database will need to be OFFLINE while its files are copied to the new location.

Alternatively you can present the new drives, shut down SQL Server, copy all the files to the new drives, unmount the old drives, mount the new drives in the same folders or drive letters as the old drives, and restart SQL Server.

In both cases take backups of your databases before you start DO NOT delete any files from the old drives until you have sucessfully migrated to the new drives and taken new backups of your databases.


  what I need to achieve now is to force one of the available HA technologies to create a copy of my DB set into the same SQL Server instance.


To do that, use Backup/Restore, not Transnational Replication.  Replication is more complicated, expensive, and does not support tables without a primary key, or all database objects.  So, for each database:


Place Database in Full recovery mode
Take a Full Backup and restore it with a new name and location without recovery
Take a Tail Log Backup of the source database (taking it offline).
Restore the Tail Log Backup on the new database with recovery.
Rename or drop the old database
Rename the new database (back online).
Restore the desired recovery mode of the new database.