Ok this is weird.
Came up as an unknown disk of double the correct size regardless of how it was connected. Tried through the Quickport and directly to the mobo. Tried connected at power on and after booting. Tried different port on the ICH controller. Always the same. One thing I did notice is that, whilst the drive appeared correctly in the Matrix Storage Manager, in device manager it appeared as simply "Volume0" rather than the drive's model number as with the two internal drives - really weird. Almost as if the controller thought the drive was half of a RAID1 volume or something.
Now I've just uninstalled the Intel drivers and let the built-in one redetect everything and it's fine. The original PIO Mode problem is gone (for now at least) and all drives are showing as Ultra DMA Mode 6, including the external one which now comes up correctly. In addition, I did used to have hotswap issues with the external dock whereby the drive would take ages to disappear after it was powered off whereas now it goes after a few seconds which is much better.
Will keep an eye on it.