Deep learning models for SAR oil spill segmentation often fail to generalize across regions due to differences in sea-state, backscatter statistics, and slick morphology, a limitation that is particularly severe along the Peruvian coast where labeled Sentinel-1 data remain scarce. To address this problem, we propose \textbf{MORP--Synth}, a two-stage synthetic augmentation framework designed to improve transfer from Mediterranean to Peruvian conditions. Stage~A applies Morphological Region Perturbation, a curvature guided label space method that generates realistic geometric variations of oil and look-alike regions. Stage~B renders SAR-like textures from the edited masks using a conditional generative INADE model. We compile a Peruvian dataset of 2112 labeled 512$\times$512 patches from 40 Sentinel-1 scenes (2014--2024), harmonized with the Mediterranean CleanSeaNet benchmark, and evaluate seven segmentation architectures. Models pretrained on Mediterranean data degrade from 67.8\% to 51.8\% mIoU on the Peruvian domain; MORP--Synth improves performance up to +6 mIoU and boosts minority-class IoU (+10.8 oil, +14.6 look-alike).