Cracked it! And this wasn't in any of the documentation.
I called technical support and they told me to hold the red button at the back for a couple of seconds, which would force the firmware to load onto the disks.
This didn't work, and they then informed me that the Hitachi Disks I was using were not on the compatibility list, but they seemed to indicate that there was a good chance it should still have worked.
We then discussed how the previously used disks should be formatted, where I had already removed all volumes and partitions in Windows disk manager, using a USB to SATA hard drive adapter, and also used diskpart to clean them after following an enclosed leaflet.
I think this next bit is a red herring, but I'll include it for completeness of what I did.
I then plugged the drives back into Windows, using the USB to SATA hard drive adapter, and formatted the volumes, but did not assign a drive letter.
When this still didn't work, I started to mess with the red button on the back of the device. I held it for a couple of seconds, but still got the red light. Then I held it for ages, until the red light still appeared.
Then I gave it a very quick press, and bingo everything kicked into life and the firmware started to transfer itself as discussed, where the red light flashes instead of staying lit. This process takes 10 minutes or so.
I now have a fully functioning NAS.