L.A.
Wow, S., it seems you've done just about everything I would have done... the mitts or socks seem like the best. That way if she scratches she's just "rubbing" the area. I would look into an allergic reaction to the detergent you may be using on her laundry... things she has skin contact with everyday... or perhaps the bath soap, get or lotion you use.
Otherwise, just keep moving her hand, gently away and put her woobie next to her when you see her reaching to "scratch". Eventually she will hopefully replace the woobie for the skin area she is scratching.
Best of luck.
Lily