Changing to 12v just because someone sold you a crap 24v inverter seems illogical. You have now caused a whole series of unnecessary problems for yourself.
The 24v stator will work at 12v but performance will be dreadful and you will be stalled all the time. It will possibly be marginally better in light winds and instead of 1W you may get 2W but up in the sensible wind region it will level off at a small current and you won't get it to do much more no matter what the wind is.
The Otherpower 10ft turbine as originally designed was a bit marginal on magnet and I think the stator they sell is based on the later version with bigger magnets. For 24 or 48v the rectangular magnets are adequate except in very windy areas with furling not set right.
The 12v case is more critical on magnets as the diode drop is high relatively to the others and also any line resistance is going to be very more significant.
It will still work perfectly well with the rectangular magnets and will be far better than attempting to use the 24v stator. The only thing is that you will need to watch the furling very carefully indeed and from recent discussions I suspect that if you are in a good wind area you may need to increase the offset to get it to furl safely with that stator.
Flux