Lots of thoughts here!

But I can't figure why it is cogging.  I just did something just about like half of that.  4 mags and 6 coils. It does not really cog at all.  The best I can figure is this rotor is sticking out between the magnets and messing up the works.

The N and S drawings are skewed as far as N and S are concerned in the same time frame.  I think.  The photo shows every other magnet lined up with a 'tooth'.

What do the top of the 12 coil 'teeth' look like?

The magnets look set INTO a laminated slot.  That shorts the flux path, so the magnetic field is bypassing the coils by just going around them straight into the laminates.  Getting rid of the laminates between the magnets will force more of the flux to go through the coils.

I bet if you pull out the magnets, turn the O.D. of the rotor down to put the magnets on top of the teeth, and epoxy them on top of the teeth...
The ouput will go up and the cogging will go down.

I keep thinking about an inside-out 3-phase arrangment.
It could work here too... I think...
http://www.fieldlines.com/story/2005/5/4/15729/16162
http://www.fieldlines.com/story/2005/7/4/34446/17324