I just applied the modification as described by the OP to the bridge pickup on my 2012 LP Special, and it worked perfectly: no hum when the switch is in the center position and both pickups are "on."
On my pickups, there is a hole in the corner of one bobbin and an adjacent hole in the brass base plate through which the wires are routed. Consequently, flipping the bobbin required de-soldering the black and white lead wires that join the pickup windings to the shielded 2-conductor hookup wire. It also required a new hole to be created in the corner of the bobbin directly opposite the original hole. It also required flipping the base plate to align with the new bobbin hole. The base plate was bent slightly along the row of holes to hold the magnets in place, so the base plate needed to be bent a bit in the opposite direction. Finally, two new holes needed to be put in what is now the bottom bobbin to accept the base plate mounting screws. The bobbin material is easily drilled by twirling a No. 11 Exacto blade to locate the hole. This is sufficient for the mounting screws. For the hole in the corner of the bobbin, just use successively larger drill bits twisted by hand.
Because I needed to desolder anyway, I thought I'd experiment. I flipped the bobbin, flipped the magnets, and I also reversed the wires: originally, the white lead wire was connected to the braided metal shielding wire which was soldered to a grounding lug attached to the base plate with a screw, and the black lead wire was connected to interior signal wire covered with black push-back cloth. I just swapped the attachment points of the black and white lead wires.
No surprise, the hum was not cancelled in the middle position. By reversing the wires as well as the magnets, the rotation of the coil relative to the magnetic poles was unchanged. If you're familiar with the Right Hand Rule (fingers coiled like you're making a fist represent the coil, thumb pointing straigh up to represent North) it makes intuitive sense that all I did was rotate the whole pickup (i.e., the whole right hand) upside down.
Just for fun, I left the wires where they were and flipped the magnets back to their original position. As expected, this put the pickup out of phase in the middle position (reverse wound, matching polarity), which sounded really awful.
Lastly, I turned the magnets back around to the OPPOSITE of their original position. (BTW, both magnets were marked on one side with stripes of blue ink to represent the matching poles. The sides with the blue markings were not orignally visible because they were placed against the metal bar through which the pole piece screws are threaded.) I also resoldered the lead wires back to their ORIGINAL locations.
Success! The bridge pickup sounded no different by itself than it did originally, the bridge and neck pickups are in phase, and when the selector switch is in the middle position there is no hum at all. I never really found the center postion on my humbucker equipped guitars to be very interesting, but the middle positon with RWRP P90s does provide a very musical and useable sound - the hum cancelling is a just a bonus.
