On the ’Advanced’ page of the BIOS, there was a switch for the Onboard LAN Boot ROM, and by default it was set to disabled. I switched it on and can confirm that ATASX works on this board.
I now see the ATASX documentation does make a mention of this in passing, saying ”you have to activate the ability to boot from network card”. So this was a simple case of RTFM on my part. :)
I’d still be interested to know how if at all this’ll work with an SSD.