Use the ADD option when you import and your folder names and file locations will not change
Bob has you pointed in the right direction.
You have already copied your images to your hard drive and have already organized them into the directories you want.
At this point all you need to do is import the files into the catalog from where they are using the "add" option.
If you use any of the "copy" commands the files will be moved to other locations using the default new folder names (or user-configured new folder names).
Thanks you guys. That really helped.
Actually, I am moving all my files and putting them on an external drive, but I'd rather move them from one drive to the other within Lightroom, than rename them