I ended up royally messing it up. 😆
First I tried completely taking the thing apart in order to fit it into the cable routes under scratchplate, which *did* get rid of a lot of the noise but broke every time I pushed it into the route, and I ended up applying that much insulation that I couldn't get in to fix it. This was only connected to the bridge pickup also.
Second attempt with another spare pickup, I tried to simply wire the dummy coil to the jack socket and stick it in the control cavity, thereby affecting both pickups (both are the same polarity, no humbucking middle position for me). For some reason this made the noise worse.
As such I gave up. If I get hold of another spare CIJ pickup I'll give it another shot, but I'm leaving it for now, I don't have the patience. I'll be going with the first method again though, seeing as before I broke it it did yield very impressive results.