How to raise capacitor voltage to use a capacitor bank as a battery?
Although the charge is linear to the voltage, the energy varies as the voltage squared. This means you only need to swing between V and V/2 to use 75% of the energy capacity. Swinging over a wider voltage range gets you little extra energy, with a wider range needed at your converter, so it's probably not worth doing.
It's not a good idea to stabilise a 3-13 V swing to 12 V if you have alternatives, as that involves both bucking and boosting. Far better to do one or the other, so 5-10.8 V up to 12 V, or 13 to 27 V down to 12 V.
With suitable converter circuitry (multiphase) and with only small voltage ratios (max 3:1) you ought to be able to achieve over 90% efficiency.
Whether it's worth replacing something that's simple, economical and well tried and tested like a car battery with something expensive and complicated is another matter.