Not 100% sure but perhaps having the pickup rewound would be the best option. It'll look the same but be 'different' underneath. I don't think the J pickups in these were designed to be used solo, more as a touch of seasoning of the P pickup.
Stuff sold by both shops are on commission so I suppose someone could have it in both shops at least in theory, though you’d be annoyed if you turned up to the wrong one to play it!
Silly question time because I can’t be bothered to look. I have six presets saved to the pedal which I can see on the desktop editor plus a few others saved. I can’t drag and drop them to switch them to the pedal so how do I put some of them on my pedal memory using the desktop app?