AFAIK, FAT32 has attributes but not permissions.
It would be nice if the attributes were preserved, but I haven't
experimented with all possible combinations of file system types,
so don't know what happens in detail.
Since FAT32 doesn't have permissions, there is no place to store
that information.
The OS supports (a rather miserable) FAT32 to NTFS convert
utility. But I don't know of a way to go from NTFS to FAT32.
Google says there are some third-party utilities for that,
but you'd need to check the results pretty carefully.
They're not likely to have as detailed a log as you get with Robocopy.
I think I would be going back to the robocopy log file,
find out how extensive the damage is, before getting too excited.
If it won't copy System Volume Information, that's not a big deal.
When the new copy of Windows boots up (on its own without the
original disk present), you can turn System Restore off and on
again, and that should clean out a fair bit of System Volume Information.
And since VSS doesn't keep persistent files in there, you don't
have to worry about that. And losing some CHKDSK log file that
is sitting in there, isn't a big deal either. So not copying
a folder like that, isn't a big deal as far as the function
of the OS goes. It's true you don't get to keep your
System Restore points, but then, you still have the
old OS disk if you need it for emergencies.
It's possible Linux would do a good job. Again, I don't know if
attributes are preserved. Certainly permissions are not
preserved, but we don't care about that anyway, as the
target partition is FAT32. Only the treatment of the
attributes would be worth verifying.
It's a situation ripe with experimental possibilities.
Many routes, lots of testing to do.
When you're finished, you'll likely need a "fixboot"
for that FAT32 partition (done from Recovery Console).
And if you aren't careful, probably setting the
boot flag on the partition, for that disk.
Paul