Ultimately, it's hard to give an accurate "watt hour" rating on a battery because the voltage decreases as it's discharged
Actually, that's why I measured the discharge (in wattage) in real time. And that's why I know that the light heads I used during measurement really do consume ~2.5 low, ~5-med, ~10-high watts during testing. Discharge curve means little in a regulated circuit -assuming it regulates.
Whether its 1.25A at 8V or 1.66A at 6V - it's all ten watts to me. No you can measure watt-hours - accurately - as i already have.