Dimensionality reduction is an important task in high-dimensional data visualisation. Among the popular algorithms for achieving this is t-SNE, which aims to preserve local neighbourhoods in the lower-dimensional embeddings. While t-SNE traditionally works in Euclidean space, embedding in hyperbolic space offers several advantages, specifically for data of arbitrary size and exponential growth, such as tree-based structures. We propose a new solution to approximate and accelerate the calculation of t-SNE gradients using a uniform grid structure. This new method produces embeddings with better neighbourhood preservation than previous solutions, while also providing better runtime performance.