Current 3DGS compression methods largely forego the neural analysis-synthesis transform, which is a crucial component in learned signal compression systems. As a result, redundancy removal is left solely to the entropy coder, overburdening the entropy coding module and reducing rate-distortion (R-D) performance. To fix this critical omission, we propose a training-time transform coding (TTC) method that adds the analysis-synthesis transform and optimizes it jointly with the 3DGS representation and entropy model. Concretely, we adopt a hierarchical design: a channel-wise KLT for decorrelation and energy compaction, followed by a sparsity-aware neural transform that reconstructs the KLT residuals with minimal parameter and computational overhead. Experiments show that our method delivers strong R-D performance with fast decoding, offering a favorable BD-rate-decoding-time trade-off over SOTA 3DGS compressors.