I had a look at your files using Paint.net which I use for image editing and sure enough you've got lots of jagged edges.
But i could smooth them out and make them go away, so I'm not sure why that hasn't worked for you unless you can't see them with Photoshop.
I've never tried to use Photoshop for editing DDS textures, but I know Paint.net does it well, so I'd recommend trying it instead. It's free software, so it can't hurt to try it.
As for your ghost necklace, there's a bit of Voodoo going on with modding DDS texture files.
You think you've gotten rid of every last trace of something, in this case the necklace, but actually you haven't.
To test it, you can blank the entire file, then you'll see no trace of the necklace anymore.
This means you've missed some of it, and you'd be amazed how much extra "cleaning" you have to do sometimes to get rid of these ghost outlines.
