Complete discharging of Initially charged capacitor through Inductor
Assuming a perfect inductor and capacitor and ideal swiches, you cannot "speed up" the process.  The capacitors in parallel (C18 and C20) will act as a single capacitance, as will C19 and C21.  If there were no series resistance, the voltage and current would be exactly 90 degrees out of phase. The voltage would be maximum and current zero when you first close S2.  For a complete transfer of energy, you must open S2 and close S3 at the point where the voltage is zero and the current is at its maximum, 90 degrees from the start point at the resonant frequency.  Then, the voltage on C19 &amp; C21 would swing to a negative value, and you must open S3 when the current is zero and the voltage is maximum.  You would then theoretically have the same energy in C19 &amp; C21 that you had in C18 &amp; C20 to start with.  So as you have rightly suspected, timing is important.

In real life, switches are not perfect and capacitors and inductors have losses, as you have pointed out, so the transfer of energy will be imperfect.