An always available option (at every subscription level) would be to setup a regular database connection, import the users there and remove the use of the custom database connection from your client application. However, importing the users would imply they would have to reset their passwords.
If you really need the process to be transparent to the end-users you could consider using a custom database with migration enabled. Although this still requires a paid subscription it is currently available for all paid subscriptions levels while custom databases are only available at the enterprise level.