Efficiently improving efficiency.

High voltage is the arch-enemy of high current. (for a given power level). Therefore to decrease current and increase efficiency at a given power level the capacitors must not be fully discharged. There must be residual voltage remaining at both phases. The energy in J [dis]charging a cap c from v1 to v2 is given by $1/2$c (v1^2-v2^2).

Charging a LC circuit from v1 to v2 requires a maximum current proportional to v1 - v2. But there is more energy transferred at higher voltages, proportional to v^2.

But this won't work.