I swapped out the flat bars on my fat-bike for Salsa Woodchippers (modified drop bar) and added a Ritchey adjustable stem to bring the bars up slightly. I've ridden thusly for 6 months including a back to back century and miles on the windy beach (hence the drops, to get low into wind).

Unlike flat bars, drops offer a multitude of hand positions. It's not an inexpensive solution because I also went to road levers and bar end shifters. But a smart mechanic at an LBS could fix you up inexpensively by using takeoff parts from an older road bike. You'd likely have to buy an adjustable stem. Bar ends ("bull horns") are ok though they get your hands away from brakes, shifters, and they can snag clothing, etc.

Another think you can do is take pipe insulation foam and wrap inside (towards stem) to give your hands a larger comfortable rest space. I did this for several months till I switched to drops.