Actually, I had some pictures still online...
Here's the pickup as it was, underneath. It actually had copper shielding to ground teh polepieces, but clearly it was not touching all of them (use a multimeter and you can verify that).
From the top: some copper shielding that was grounded, and now I just needed to get it to touch the polepieces. I tried to add a bit of solder between polepieces and copper (adding another strip of copper just tangent to the polepieces), but it didn't stick... so I went with plan B.
This is plan B: the copper strips across the polepieces.
I don't have pictures of the polepieces with the nail varnish, but it works

I painted them black at some point, then silver.