jaquith, thankyou. All drivers obtained from www.fic.com.tw and other places failed to allow operation at 1366 x 768 or 1360 x 768. However, upon booting from a Puppy Linux 4.2.1 CD, I was able to specify 1360 x 768 and POW! - up came Puppy Linux on a perfectly crisp clear 1360 x 768 wide screen.
So, clearly both the motherboard integrated hardware and the Samsung BX1931N LED monitor support that resolution.
I then noted down the video scanning parameters used by Puppy, rebooted into Win XP, ran a few EDID tools, was able to generate sensible timing parameters and an override .inf file, which does not appear to be overriding anything. In particular, I am unable to find in the Windows registry anything remotely related to the contents of the override .inf file.
Any further guidance on how to force the FIC AE31 motherboard to utilise my known-to-work-under-Puppy timing parameters would be appreciated.