Can transformers be used to adjust capacitors?
The short answer is "no."  A capacitor is, fundamentally, an energy storage device. The energy density (joules per liter) of a particular kind of capacitor (film, electrolytic, whatever) is roughly constant, whether a particular module is optimized for high voltage/low capacitance or for high capacitance/low voltage.  Transformers let us trade voltage for current, but the energy entering the low voltage side is still the same energy coming out the high voltage side.  So the same volume of capacitance (and thus the same approximate materials and cost) will be needed to do the same job, regardless of which side of the transformer the capacitor is installed on.

More broadly, you may be interested in the concept of a Pareto Frontier.  The phenomenon you describe of being unable to optimize multiple qualities simultaneously, and thus having to make tradeoffs among them, is pretty much universal.