By building and simulating neural systems we hope to understand how the brain may work and use this knowledge to build neural and cognitive systems to tackle engineering problems. The Neural Engineering Framework (NEF) is a hypothesis about how such systems may be constructed and has recently been used to build the world's first functional brain model, Spaun. However, while the NEF simplifies the design of neural networks, simulating them using standard computer hardware is still computationally expensive – often running far slower than biological real-time and scaling very poorly: problems the SpiNNaker neuromorphic simulator was designed to solve. In this paper we (1) argue that employing the same model of computation used for simulating general purpose spiking neural networks on SpiNNaker for NEF models results in suboptimal use of the architecture, and (2) provide and evaluate an alternative simulation scheme which overcomes the memory and compute challenges posed by the NEF. This proposed method uses factored weight matrices to reduce memory usage by around 90% and, in some cases, simulate 2000 neurons on a processing core – double the SpiNNaker architectural target.