I hope that 10,000 amp hour battery light was a typo as anything with that large a battery would weigh as much as your bike. 850 lumens is easily achieved with a CREE XML-T6 LED which is common in some lights and flashlights (I own several). 1000 mAh batteries are also common but if you can find a light that uses the 18650 Li-ion battery and allows you to switch batteries easily, you might do well using one of the better Japanese batteries like Sanyo or Panasonic which are available in 3,400 mAh capacities. That will give you far more runtime between charges than 1000 mAh for the same lumen output.