I'm still confused. There are pieces of this that do not fit with what I remember.
In the original V2, they used a Kerosine powered engine to build the fuel pressure. It was effectively a separate engine that ran at the same time as the main rocket engine.
My understanding of the turbo pump is that it has it's own combustion chamber that burns fuel as if it were a jet engine.
Like this. 
The article to which you linked me appears to indicate that the turbo pump runs entirely off of the expansion of fuel heated by the nozzle. Sort of like a steam turbine.
If that is the case, it's easy to see why a steam turbine design would be less powerful than a combustion powered design.
Were we using this sort of steam expander design instead of a combustion driven design?
That seems like ignoring low hanging fruit.
‘What all the wise men promised has not happened, and what all the damned fools said would happen has come to pass.’
— Lord Melbourne —