It sems to me you are confusing two things here.
There is the move process, and then there is the need to create and maintain backups. You can't have them combined, you can't move the originals to the locations where the backups are. Then you have, in reality, no backups. And you MUST have backups.
There is also no way for Lightroom to move just the "non-redundant" photos.
I think you need to seriously reconsider the goal of this effort. I suggest you decide to have backups on one external HD and originals on another external HD. That is something we could provide instructions for, if you want to do this.
OK, yes I'd love to have instructions on how to backup all my photos on to another external hard drive.
Backing up photos to a different drive can be done via your operating system (copy and paste), but this is a one-time only backup; or better yet by third party utilities that perform automated and regular backups.
You must also make backups of your catalog file, which can be done in Lightroom by turning on the backup option in Catalog Settings. This will cause Lightroom to make backups of your catalog file at some regular interval that you specify (daily, weekly, etc.) When you exit Lightroom, a catalog backup dialog box will appear and give you the option of where to place the backup catalog file, you must specify that this backcup goes to a different disk than the original catalog file.