Structure-prediction methods routinely sample highly distorted, far-from-equilibrium configurations, which can require conventional machine-learning interatomic potential (MLIP) workflows to include similarly unphysical local atomic environments in the training data to maintain stability during the search. We show for the complex perovskite surfaces (110) and (001) that foundation MLIPs, fine-tuned on minimal data sets containing only physically reasonable structures, can serve as robust backbones for evolutionary structure prediction. We systematically benchmark fine-tuning strategies and identify freezing the representations and tuning only the readouts block as the most effective strategy in the low-data regime. Fine-tuning on as few as $23$ structures is sufficient to perform evolutionary searches on reconstructed (110) surfaces. For (001), a lightweight active-learning approach based on as few as $20$ fine-tuning structures enables the prediction of new low-energy candidate structures for the ($\sqrt{5}\times \sqrt{5}$)${26.6}^{\circ }$ reconstruction.