I know this is an old thread, but I did figure this out by doing something similar. I wanted to take my OG XBox saves from a 360 back to an original XBox, because I didn't like some of the oddball things the 360 was doing with emulation. I had a ton of games that had way too much progress to let go.
1. Go to the Eaton Works FatXplorer website and download the latest Beta release. Unzip the file to the directory of your choice.
2. Connect the 360 HDD to a PC with the Hard Drive Transfer Cable
3. Run FatXplorer Beta executable as an
administrator and click on "Devices" in the upper left corner. This did not work for me until I ran as administrator. It seems to only give access to all the folders when you are an admin.
4. Click the Icon for your HDD.
5. A new window will open. In the "Mount Options" menu, load the device. You will then see all the drive partitions.
6. Click the "Content Partition" and then the mount button. Mine defaults to "X" for the drive letter. Just make sure it is an unused letter and you will be fine.
7. A new file view window will open up with the newly mounted partition.
8. Follow this path on the mounted partition.
9. These are your game saves. Copy them to a folder on your desktop.
10. Close the file view window and click on devices again in FatXplorer.
11. Again click the icon for your HDD.
12. Click "Unmount" in the new window.
13. If Windows is still seeing the USB drive, be sure to eject it before removing.
14a. If you are moving to another 360, follow the above steps with the other hard drive, but at step 8, copy the saves from your desktop to the path on the target drive.
14b. If you are moving to an original Xbox, there may be multiple methods, but I will tell you mine. Mine is softmodded via the "How To Softmod An Original Xbox! - Rocky5 USB Method" YouTube tutorial by Archades Games and then I use Filezilla to transfer over the saves. Be sure to follow the YouTube tutorial by Blaine Locklair on how to set up Filezilla or your transfers may fail. Your OG saves should be under /E/UDATA. Just drag the saves from your desktop to the directory in Filezilla and you are all set.
Sorry about the lack of links. As a new user, I am limited in what I am allowed to post without getting flagged for spam.