OK, I was hoping you would give the actual locations of the folders but I'll try to explain this as best I can.
The portable restore files for 360 backups are: arestore.exe and arestore.loc
These files are automatically copied to external drives when you create a backup set onto them
For backups on local drives they are not copied anywhere but if you search your system you can find these 2 files and make copies of them yourself.
For these files to work, the backup folder has to have the default name of "N360_BACKUP" and the portable restore files have to be located one folder level "up" from the backup folder.
Lets say you had an external drive with the letter G
In the "root" of the drive would be the 2 files. (root of the drive means not in a folder or subfolder.
G:\arestore.exe and G:\arestore.loc
The backup folder would be G:\N360_BACKUP
Thats what I'm trying to say by "the portable restore files need to be one level "up" from the backup folder.
Then you can double click arestore.exe and use it to restore files out of that backup set.
See if that works for you on one of the folders that is still named N360_BACKUP.
Just be careful of the folder you have named _N360_BACKUP, don't remove the undercarrage "_" if there is another folder in that same location because you don't want to merge 2 folders together.
Dave