SMELLIE is an optical scattering calibration system for SNO+, a large-scale liquid scintillator neutrino detector. The system consists of lasers firing light through multiple optical fibres into the detector, allowing for the measurement of optical scattering within the scintillator. In order for this measurement to be possible, the angular emission profiles must be correctly modelled in simulation. A novel statistical approach to deriving these beam profiles from existing calibration data is presented. By formulating a likelihood function for the observed PMT hits in data in terms of the beam profile and other physical parameters, multiple data sets can be combined together for the first time. As a result, the statistical uncertainty and dynamic range of the beam profiles obtained have improved greatly. This work has opened up an interesting and powerful method to further improve the detailed MC description of elements in the detector such as positions of hold-up and hold-down ropes, or the reflectivity of the acrylic vessel.