For anyone with anything similar, please read on.
I left the Security & Privacy window open for a while and after a few minutes the "Enable system extensions" button just appeared.
When pressing, it asks to start the machine into the Recovery environment and launch the Startup Security Utility (on the menu bar once you've booted into it as per the on-screen instructions), and then to enable the user management of kernel extensions.
After completing this and booting back into MacOS, the driver is no longer listed in the Disabled Software section of System Information and the DDJ-1000 is now an option in Rekordbox. All working good.

