The IceCube Neutrino Observatory relies on an array of photomultiplier tubes to detect Cherenkov light produced by charged particles in the South Pole ice. IceCube data analyses depend on an in-depth characterization of the glacial ice, and on novel approaches in event reconstruction that utilize fast approximations of photoelectron yields. Here, a more accurate model is derived for event reconstruction that better captures our current knowledge of ice optical properties. When evaluated on a Monte Carlo simulation set, the median angular resolution for in-ice particle showers improves by over a factor of three compared to a reconstruction based on a simplified model of the ice. The most substantial improvement is obtained when including effects of birefringence due to the polycrystalline structure of the ice. When evaluated on data classified as particle showers in the high-energy starting events sample, a significantly improved description of the events is observed.