Apologies - I misread the section you had posted in for some reason…
It works the same way as on PS, but you can only see the files if you’re still on 360; XB1 is, as you’ve noted, rather opaque and unforgiving when it comes to individual save files.
You could try forcing a resync of the XB1 by doing a full power reset (unplug the brick from the wall etc.) or - a more extreme option - a factory reset keeping the games and apps on the drive.
The latter means you’d need to re-add your GT to the XB1; then, whenever you started a game, the system would first sync those saves back from the cloud saves. No guarantees that this would fix the problem though - it really depends on when the profile.bin file got corrupted, and whether the sync’d version is before or after that corruption.
I’m not sure if the loyalty rewards can be fixed by the support staff or not, unfortunately. I do know that you can’t re-enter SHiFT codes, but the support staff can at least check your reward history and see what you’ve earned in the past.