Weight-Decomposed Low-Rank Adaptation (DoRA) extends LoRA by decoupling weight magnitude from direction for more efficient LLM fine-tuning. However, the computational overhead of computing row-wise norms of the adapted weight matrices creates significant memory challenges, especially at high ranks and across hundreds of adapted modules. This work introduces a factored norm decomposition that eliminates dense matrix materialization by computing squared norms through base, cross, and Gram terms with O(d_out r + r^2) complexity. Additionally, fused Triton kernels combine the four-kernel DoRA composition into a single pass, achieving approximately 4x memory traffic reduction and numerical stability in near-unity rescaling regimes. These optimizations make high-rank DoRA feasible on common single-GPU setups for large language model adaptation.