Eventually, however, I stumbled across a solution almost too simple to seem likely to work: an in-place upgrade of Windows 7. Everyone simply wiped/reinstalled Windows.
Myriad internet searches also turned up lots of other people with the same problem, but no actual solution. My usual remedial measures, after poring through setup error logs and all that fun stuff, were completely unsuccessful in this instance.
The installation failed in the SAFE_OS phase with an error during REPLICATE_OC operation A screenshot of the setup error message which repeatedly plagued this machine The error message they were receiving was: This week, a client brought me a Windows 7 PC which refused to upgrade to Windows 10, despite their having reserved a license long ago for the OS and attempting to install it repeatedly.
