The 11.1v 1500mA may be to small. It could work, but not for long if it does. I recommend a 12V SLA (Sealed Lead Acid) 5Ah minimum. These batteries are fairly small only weighing a few less than 3lbs. I would run a 3A Fuse inline on the positive side of the power cable also.
The 14.8V 1600mA would work better, like Jimmy said theoretically you could get 8hr use out of a full charge, but YMMV
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