Looking great!
You need to connect the copper shielding to ground. You've got a choice of running a ground wire from the back of the volume pot to the cavities and either soldering the end of the wire to the copper foil, or you can use a small screw and a washer, and captyure the bare end of the wire under the washer to hold it against the foil. You can run separate ground wires to each cavity from the back of a pot, or run pot to first cavity, then daisy-chain a ground from there to the 2nd cavity.
Just be careful that the wire doesn't interfere with the way the pickups sit. If you go for the screw option, I'd attach it to the side of a cavity, rather than risk it protruding from the bottom (unless you measure the amount of depth remaining and use a screw that's shorter than that by a couple of mm).