I think I have already done this, by a different method.
Isn't it what I did when I loaded the 'ArduinoISP' sketch onto my new board, wired it to my old board, then set use 'Arduino as ISP' as the programmer in the ArduinoIDE and clicked install bootloader? I thought this was bypassing the 16u2 to install it straight to the 328p, because this succeeded.
edit: For the sake of completeness I attempted to load the bootloader over usb from the IDE but I received this error
avrdude: usbdev_open(): did not find any USB device "usb"
remembering I have another Uno working perfectly, so this is not a driver issue
this makes me think the source of my problems is either the 16u2 (it did arrive in DFU after all) or between that and the 328p
Does this point to any other possible solutions or should I start writing for refund/replace?