MAX31855 assumes thermocouple (voltage-temperature curve) to be linear and with one set of coefficients for the entire range. I had a similar problem (K-type, though). What I had to do was read the "temperature" from MAX31855, if below zero, reverse-calculate thermocouple voltage (see datasheet for equation), substitute it into the polynomial equation for my thermocouple type and get temperature manually. Still was several degrees off at LN2, but got within one degree for dry ice, which was nice.
There are a series of videos on how to do this calculation right on youtube, called Thermocouple 101. I'm behind a firewall that blocks youtube right now, but search should turn it up easily.