I use 2" or 2.5" strips I cut myself from continuous bias binding. Mine is also doubled by pressing the finished very long strip in half, both raw edges hidden beneath the rolled edge of the front of the quilt and hand stitched to the back.
Your strip idea sounds like a great one for a scrappy edge! Enjoy your binding...I am not sure why people dislike this part. It's one of my favorites since I think it adds the finishing touch and means I'm just about done :D :D :D
RETRO