You can increase the voltage by dividing the copper finer - more turns of finer wire.  But you decrease the current in proportion.  So you DON'T increase power.  With the same magnets and RPM you still get the same power and the same resistive losses.

Even if you're changing the thickness of the coils there's an optimum point:  Adding copper increases voltage, but the necessary increase in gap reduces flux and thus reduces voltage.  There's a peak to the curve, which is where you want to be.  With any particular thickness of stator and gap between magnets you get a given amount of power at a given RPM, regardless of how you run your current/voltage tradeoff.  (At least to a very good first approximation.)

You CAN increase power by increasing the RPM - raising the voltage without changing the current.

You CAN increase power by "paving" more of the space between the magnets with copper - filling in the gaps with another phase coil, splitting the magnets into more poles and adding more turns (providing they're in space that would otherwise would not have had copper), etc.

But absent an RPM change or a "paving with copper" change you get zilch.

Having said that, there are other things about voltage changes that can change power delivered to the batteries:

 - Raising voltage means you lower current in the wiring.  That makes no difference to the limits from thermal losses and burnout risk limiting in the genny itself.  But in the transmission lines from the jenny to the batteries you gain big-time.  Multiplying the voltage by 10 divides the current by 10 and divides the line losses by a factor of 100.  On even a moderate run with wires thick enough for welding this will make up for transformer losses with a lot left over to charge batteries faster.  If you built two mills that are identical except for 10 turns in the high-voltage model for each turn in the low voltage one, that's probably where your gain came from.

 - More turns of finer wire means a drop in eddy-current losses in the genny, which reduces load and heating, which lets the prop spin a bit faster, which increases voltage a bit.  Even a small voltage rise can map to a significant rise in charging current, while the lowered thermal losses allow the mill to run the bit faster without burning up.  So you'll see this improvement even without adjusting furling.  But this is a rather small effect in the 24-240 volt change.

Your blade extensions will increase the energy capture in low winds. What we really need to know is how well you are performing at present.

Do you have any idea of cut in speed at present?. I am reasonably happy with the blade extensions, it does reduce the solidity and that will help you to get a bit more speed than building a new prop to the same tsr and with the new diameter.

If cut in speed is your issue then you need a few more turns on the coils. If your cut in is ok at about 7 mph and you are reaching stall then the new blades may get you out of it and things may really come to life. If you are not stalled now then the improvement may not be spectacular but you will pick up the extra power from the increased diameter.

If the thing works well at cut in and then fails to increase current rapidly with wind speed and the prop fails to speed up then you must suspect stall. If the thing picks up speed rapidly then stall is unlikely.

I think you said it was 24v. Try it at 30 or 36v by temporarily adding an extra 6v or 12v battery. If the top end power ( not amps, volts x Amps) increases then that will indicate stall.

I don't think you will see any benefit from the transformer unless you have a very long cable run with thin wire. If you need lower cut in then just increase the number of turns a bit and use slightly thinner wire and accept a lower maximum safe output.

If you are too slow now and you are trying to cut in at too low a wind speed ( below 7 mph) then you would do better with a few less turns of thicker wire.

You don't have enough magnet to drastically alter the maximum safe output of the alternator so don't try for too big an increase in blade diameter. it may work well enough in light winds but you may not be able to control it in higher winds. Any increase in blade size may require an increase of alternator offset.

Flux

This makes low frequency transformers large and costly. For windmill alternators intending to use transformers you really need to start with lots of poles. Things such as AWP don't work out too badly but starting with 12 poles on a machine over about 8ft makes it highly unlikely that you will see benefit from a transformer unless you have hundreds of yards of cable.

Digressing a little, transformers work perfectly well over the audio range as long as you choose the flux density at the lowest frequency. The flux density then becomes inversely proportional to frequency and the low flux at the higher frequencies prevents the core loss being a problem. For decent high frequency response you need to sectionalise the windings to reduce leakage reactance, but this is not really about audio transformer design.