BTW I think you may use Multi-Rename Tool for such operation.
Instructions:
1. Create temp folder e.g. $mrt$ in folder where you want to rearrange files and move all files to rearrange into it.
2. Enter $mrt$ folder, select all files and open Multi-Rename Tool (Ctrl+M).
3. Set
[N] as name template,
[E] as extension template, check flag
regex in 'Search & Replace' block and specify to replace
^ with
..\\ (dot dot slash slash, exactly as I write).
4. Rearrange files in list as you wish using dragging.
5. Press
Start!
As result, TC will move files back to source folder,
but in specified order, as you need.
Oh, of course, 6th step is to remove temp folder $mrt$!
I tested it on FAT-16 drive (reformatted temporary drive to it) - works fine!