Yes Gerry, things often end up in strange places here and sometimes cause confusion.
I will have one more go at trying to explain the issue that is bothering you.
In your particular example with the coils producing 1 volt you are quite right that the single phase case has a far higher voltage and for a given speed and would be producing output long before the 3 phase case.
Your example is totally fictitious, you have arbitrarily chosen the same coils for the single phase and 3 phase case.
I tried to explain previously that the number of turns per phase is the factor that decides voltage. For arrangements with different numbers of coils per phase the turns in a coil will be different. You can make 6 coils of a 12/9 3 phase produce the voltage of one phase of a 12/18 or 12/36 three phase winding by altering the number of turns per coil.
Forget 3 phase for a moment, concentrate on the single phase case. The obvious one is the case where you have 12 coils in series and with your example you would have 12v.
It is perfectly possible and in fact very common to produce that winding with only 6 coils. If you still want 12v you will need to wind each coil with twice as many turns. you can do this because you have extra space that you can use where the missing coils would have been. Ignoring minor differences the 2 windings are exactly the same.
Now going back to the 3 phase case, you can wind the coils with more turns to still have the same ac line or phase volts so you can achieve the same cut in voltage at a given speed as the single phase case. The turns per coil will be different for single phase, 3 phase star and for 3 phase delta. Also the wire size will need to be different in the 3 cases.
Volts alone produce produce no power, you must have a cut in speed above battery volts and the current that flows will be dependent on the voltage difference and the effective circuit resistance. Power is the product of battery volts and the dc current flowing.
The fact that you have had to use different sizes of wire to fill the same space with the desired number of turns adds a confusing factor that is rather more difficult to grasp and you need to know the way in which each type of winding delivers current via the rectifier.
Just bothering yourself about integrals under curves is not going to solve your problem, that integral only affects voltage.
I hope this helps, it is my last attempt to explain.
Flux