This would be easier with a diagram, but hopefully this helps...
You probably don't need to swap any magnets, though you could. What probably has happened is this:
Think of a H-H guitar. When you split the neck humbucker, you usually want the SCREW coil to be active, which is the South coil. This is the coil that is closest to the neck, and hence the loudest. When you split the bridge humbucker, you usually want the SLUG coil to be active, which is the North coil. This is because, again, it's the loudest as it is the one closest to the neck. You could split the screw coil in the bridge position, but it will sound thinner, more trebly, and weaker. Also, now the middle split position will hum cancel.
So what you've probably done is split the "wrong" coil in the bridge humbucker, and that is out of phase with the middle pickup. The diagram you linked to has the N coil active when split in position 2, if I read it correctly, and that's the same polarity as your middle pickup and will be out of phase.
OR alternatively, perhaps you are splitting the humbucker correctly. In this case what you would need to do is swap the Hot and Ground leads from the middle single coil. You should be back in phase with the bridge at this point, but out of phase with the neck. If that happens, go swap the Hot Ground leads on the neck single coil as well, and you're all good!
A diagram of what you actually did (not what you were trying to follow, but a picture of drawing of what you actually did) would be helpful. Bare Knuckle uses different color coded wires for pickups than Seymour Duncan does, or Gibson, or Fender, etc, etc. So it can be confusing unless you draw out a diagram with labeled color codes and everything. I'm attaching two pictures as an example of what I mean, from when I was swapping pickups in my Mayones Regius a lot. Note that Seymour Duncan and Suhr (I was using some Suhr pickups) use the same color codes. Notice that I wire the neck and bridge humbuckers "opposite" of each other, because I want to coil tap the opposite coils.