I'm attempting a synthesis of this thread and the dynomometer test results reported
on this thread.
A >14V supply gives 40-50% extra power output compared to a 12V supply.
So while the flat 12.5V profile between 0.4 and 1.0Ah is nice, keeping the battery at less than 0.1Ah discharge seems to be the best competitive policy.
Caveat: My knowledge of battery technology is limited, so corrections are welcome.