Tim, I'm confused about your problem, but I would like to help.
If you are moving files from one computer drive to another they would normally be shown sorted by file name in Windows Explorer. Is this where you are looking/working?
When you use Media Center to view your files, you can setup the view any way you want to see things, such as by Artist, by Name, Track number, etc. (it doesn't matter how the files are sorted on the hard drive or card).
The views (sort order and grouping) are setup in MC. For example, if you are in MC using the Standard View, and you open "Audio>Files" you would sort by "track #" by clicking on the header for the column displaying tracks. Similarly if you wanted to view by Name, you would click on the column header "name".
I probably don't understand what you are asking. Need more info on what view you are using and what you are seeing or not seeing now.
I would suggest you use the built-in "Rename, Move & Copy Files" tool in MC and do all your work within MC.