We present the first systematic benchmark of parameter-efficient fine-tuning (PEFT) for low-resource neural machine translation (NMT) of indigenous languages of the Americas. We evaluate eight PEFT methods alongside full fine-tuning on NLLB-200-distilled-600M across 13 indigenous-to-Spanish language pairs spanning four resource tiers (357-125,008 training sentences). OFT (Orthogonal Finetuning) achieves the highest development-set chrF++ among PEFT methods (26.63) while training only 0.28% of parameters. LoRA (Low-Rank Adaptation) offers a strong efficiency-quality tradeoff (25.27 chrF++, 0.19%). On held-out test data, full fine-tuning ranks first (25.12) with OFT a close second (25.06; p = 0.43). VeRA (Vector-based Random Matrix Adaptation) and Prefix Tuning consistently underperform. These results demonstrate that PEFT is a viable alternative to full fine-tuning for indigenous-language NMT.