The generated voltage goes up with the turns ratio for a given RPM.  Resistive voltage drop is a separate (though related) issue.

If the total cross section of the wire is kept constant by resizing in proportion to the change in turn count (which is also what you want for fitting it into the slots), then at the same power output you'll get the same percentage of power lost to heating.  The current will have scaled down in proportion to the turns ratio, resulting in the same voltage drop per turn.  So the voltage drop will have scaled with the voltage.

The only thing that won't just scale is eddy current losses in the copper, which will go down due to breaking the constant cross section of copper into thinner pieces using the finer wire, thus eliminating some of the eddy current loops.  (Much like laminating a magnetic core to cut eddy current losses there.)  But this is a small part of the losses.

Now you WILL have lower current output for any given amount of power generation, and resistive losses go with the SQUARE of the current.  So if this is a battery charging application (where output voltage is constant at the battery voltage and CAPTURED energy is thus proportional to current) the percentage lost to resistance heating at a given CURRENT output will go up due to the increase in resistance.

Does increasing the voltage effect the short circuit braking properties of the turbine or will that all stay the same?

I dont know much about the whole resistance issue.  Does using smaller wire mean the turbine will have less output through heat loss?  Will overheating be an issue?

I was talking to a local motor rewind shop that said they could rewind it, but I wasn't convinced they knew what I was talking about.  I would rather be able to tell them what needed to be done, like how many turns to use and what wire size, than rely on them doing what they thought was best.

Thanks for everyones input.