I was able to dig up an original Perform 630 CD, which has the 7.1.2P software on it. I updated my Powerbook 500 system folder using the installer and it updated correctly. I now have my PB540c running System Z-7.1.1 (They didn't increment the version number, but it shows a copyright date of 1994, rather than the typical copyright date of 1993 for all other known versions of 7.1.1) & Finder 7.1.4. There were also a number of updated Control Panels & Extensions on the Performa 630 CD which work correctly on the Powerbook 500 as well.

Did they increment the version number to 7.1.2 for the PowerPC version of 7.1.2 or did they leave it at 7.1.1?