Here's a pic of my, now empty, battery box with the JJB output jack in place'
Here's another idea, on a MartinX with a Sonotone, I replaced just the braided UST for a really nice improvement in plugged as well as unplugged sound. I used a generic solid UST that I got from Amazon for about $10
I sold that one and the girl who bought it also liked the plugged and unplugged sound.