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You best bet is probably an OKR regulator at high voltage with 2x 1000mAh or better batteries.
OKR for reliability and efficiency.
High voltage because it draws let current to maintain you desired wattage.
1000mAh or better because users typically get a full day plus out of this setup and ~1000mAh.
With 2x 2250mAh Panasonic cells you should be able to stretch 2 days or more out of a charge. More if you spend a little more for the 3100mAh Panasonic NNP cells.