That should be a good combo of motor controller and battery. Very similar to mine in amps draw, and I never had a cutoff that wasn't from riding too far, like over 20 miles uphill. Cammy's first test will be if she sends hookup instructions. A lot of new battery owners are pretty confused by three wires when other vendors send no instructions at all. Pings instructions were very good, so I didn't freak out on the chargers behaviour at first. For awhile the charger will cycle on and off, balancing the pack during the first week or so of break in.
Did you find out from Cammy what kind of cells inside? If they are similar to the version 1 cells Li Ping sold last spring, it will still be a very good battery. The new 4ah cells are supposed to have a better c rate, but when tested at 1c, went a lot more cycles than the cells in my pack. This is where I get the idea that for now, 1c discharge rate is still the discharge rate to aim for. At the rate I discharge, similar to what you will do, I'm expecting at least 30,000 miles out of my battery. When I calculate what the bike costs me per mile, the battery is the cheapest item. I'm guessing I'll fry a motor or controller at least annually, and wallmart bikes can't have more than 2 or 3 thousand miles in em.