After many hours of frustration and getting *this close* to giving up on this board and INTEL as a respectable board manufacturer, I was able to eventually solve the problem through some dumb luck:
In order to flash the bios, I had to turn the Intel Management Engine on by pressing CTRL+P when prompted during the boot sequence. After choosing "ENABLED" and rebooting, the bios was able to complete the flash cycle without a hitch.
As far as I can tell, this little "gem" of knowledge isn't documented anywhere. Perhaps it was just an idiosincratic system fluke, but it worked for me. Figured I'd post it for the next person who runs into this trouble...