I had the same problem and solved it with a portable hard drive which has its own power supply and can hold a ter/bite and the battery will last for the whole trip. 3x4" and sold by HP and very light, maybe 4-5 oz. Works for me and if you shoot more than it's capacity I'll be surprised.
Cost is actually less than FD"s.

Bought my D7100 with some lenses and have excellent service from the dealer and the product. Go for it.