Fortunately, there is a very neat solution provided for us by Microsoft through the SURT for .cat, .mum, and .manifest files (only these file extensions, unfortunately, due to security reasons, I think).
.cat and .mum files, in pairs (remember that they must always be paired up, even if only one is corrupt), can be placed in the %SystemRoot%\Temp\CheckSur\servicing\Packages directory, and .manifest files can be placed in the %SystemRoot%\Temp\CheckSur\winsxs\Manifests directory, and the System Update Readiness Tool re-run. The SURT will then perform the replacement of corrupt files, sourcing good files from the directories given above, and dealing with all permission issues safely and securely.