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Maybe a not too big supercap bank combined with a small BMS protected lithium iron phosphate battery, but split by a resistor.
The supercaps generate the amps to crank the starter motor, the battery keeps them charged over time.
The resistor prevents high currents to or from the battery so it won't get killed by high recharging after starting up in the cold.
That would be lighter than straight lead acid and not have the overcharging losses.
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2011 Honda Insight + HID, LEDs, tiny PV panel, extra brake pad return springs, neutral wheel alignment, 44/42 PSI (air), PHEV light (inop), tightened wheel nut.
  lifetime FE over 0.2 Gigameter or 0.13 Megamile.
For confirmation go to people just like you.
For education go to people unlike yourself.
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