Might it work to use a 13.2v or 14.4v battery? The alternator would feed it at ~14v, which would keep it mostly charged, but it would have the ability to absorb additional power from a higher-voltage source when available.
I think cells are 1.2v, so by using 11 or 12 cells, you could make a battery that's a slightly higher voltage. I don't know enough about it to predict how it would behave, though. The charging system voltage might not be enough to maintain a useful charge in a 13.2v battery.
I'm thinking NiCd or NiMH, but only because I don't know of a source for 1.2v lead-acid cells.
Like maybe 11 of
these in series for 13.2 nominal voltage, 10 Amp-hour capacity? I guess that gets a little bit expensive, and would require some additional electronics to control charging. NiCd are supposed to be able to supply very high discharge rates (up to 50 times capacity), so CA should be significantly higher than a lead-acid battery of the same amp-hour capacity (as much as 20 times higher). Read more on
Wikipedia.
The
PC680 is my benchmark, since it has good power for applications that take relatively high starting current for small engines (BMW boxer twins). It's also certified (in slightly different form) for cranking 300+ cubic inch airplane engines, and it shows 17 amp-hours' capacity.