I doubt very much that you have stall problems so low in the wind speed especially with those thin magnets. With that size prop then you may hit stall with a dual rotor.

The bit about wire size is very confusing, I will try to explain but it is still complicated.

The voltage ( number of turns ) does determine cut in speed and the wire size will make no difference.  Now the thin wire will have high resistance and the thick one will have low resistance.

The alternator with thin wire will need to turn faster at any other speed than cut in to produce the same current. Perhaps you can imagine the high resistance one needing to run at twice cut in speed to produce 10A, the low resistance one may reach 10A at only 10% above cut in.

For the alternator alone this is simple and straightforward, the low resistance winding will be far better and will produce much more power with less internal heating.

Now the really tricky bit, the power produced by the prop increases with the cube of the wind speed as long as it runs at the optimum tsr. For this to happen the rotational speed should directly follow wind speed. If it doesn't you will fall off the peak of the prop's power curve.

To maintain ideal tsr say you cut in at 7 mph, you should rum at 3 times cut in speed at 21 mph. This is a big increase in speed and would be the sort of thing you would expect for the high resistance and inefficient alternator. Your prop keeps high efficiency but alternator efficiency falls very rapidly with wind speed.

Now look at the efficient alternator and it wants to run at nearly constant speed ( 10%  increase above cut in say) that alternator is very efficient but you push the prop so far off its peak of the power curve that you don't have enough power available to drive the alternator to the speed required to see its benefit.

There has to be a compromise, you aim to let the prop speed up enough to hold reasonably well on its power curve yet you must get a sufficient current increase from the alternator to match the power available from the prop.

A good compromise seems to be to let the prop speed double with 3 times increase in wind speed. This means that your power rises less than wind speed squared ( not cubed) and the alternator efficiency drops to about 50% at three times cut in speed.

In your case I doubt very much that you are seeing wind speeds anywhere near 20 mph so you will not see a great deal of difference whatever you do to the alternator. If you have got the best cut in then there is not going to be a lot left to chase.

As a very rough guide the best you are likely to do is about 40W at 10 mph for a decent 6ft prop. I am not sure that you can even get that with a simple pvc one.

The fact that you have tried 12 and 24v and tried series resistance and moving the magnet rotor suggests that you are managing just about all you can get from that diameter and type of prop in your wind speed.