But how should that gain in energy output be possible without making the whole system huge, too? The heat generating part of a nuclear power station only makes

But how should that gain in energy output be possible without making the whole system huge, too? The heat generating part of a nuclear power station only makes up a small fraction, most of the material is for transforming the heat to electricity and to shield off radiation. If you want to process more heat, you need more infrastructure to do so.