Fine-tuning large language models (LLMs) remains a computational bottleneck due to their scale and memory demands. This paper presents a comprehensive evaluation of parameter-efficient fine-tuning (PEFT) techniques, including LoRA, BOFT, LoRA-GA, and uRNN, and introduces a novel hybrid strategy that dynamically integrates BOFT's orthogonal stability with LoRA-GA's gradient-aligned rapid convergence. By computing per-layer adaptive updates guided by gradient norms, the hybrid method achieves superior convergence efficiency and generalization across diverse tasks. We also explore, for the first time, the adaptation of unitary RNN (uRNN) principles to Transformer-based LLMs, enhancing gradient stability through structured unitary constraints. Across GLUE, GSM8K, MT-Bench, and HumanEval, using models ranging from 7B to 405B parameters, the hybrid approach yields consistent gains across three independent runs per task and model, approaching the quality of full fine-tuning while reducing training time by approximately 2.1 times and peak memory usage by nearly 50 percent, indicating practical significance under resource constraints. A compact multilingual and low-resource study on XNLI and FLORES, using 32 examples per language, further demonstrates consistent gains under the same budget with a small and stable footprint. These results indicate a practical and scalable path toward accessible LLM fine-tuning under resource constraints.