Ideally, optimal hum rejection occurs when the EMI detected by the dummy coil and pickup are equivalent. Being in a location where the two are equally susceptible to EMI helps in achieving that. But AFAIC, the objective doesn't HAVE to be hum elimination. Mere hum reduction that makes a guitar more liveable is also a good thing. At the very least, it means that any noise-control pedals/devices being used can be set in a more generous fashion, with a much lower turn-on threshold.
Many years back, I installed a dummy coil in a buddy's Telecaster in the control cavity. It certainly didn't "kill" the hum, but reduced it enough to be acceptable, without wrecking the inherent tone of the guitar. At least that's my recollection.
So, I wonder if a dummy coil might be more successful in the LP control cavity, rather than sitting under a pickup baseplate.