Huh. So the fr-ca (eg. Quebecois) listing for support files for this >10-year-old hand-me-down HP Pavilion is still up and in search results, despite the HP site refusing to let me into an English listing because it's "too far out of support".

...the newest UEFI they offer still doesn't fix the refusal to POST with GeForce cards new enough to be UEFI GOP-native (i.e. 7xx-series and above), but at least now I know .