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While fixed-length stabilization phases are significantly more computationally efficient than static update schedules, they require task-dependent manual tuning, risking either the waste of prior knowledge or severe overfitting. To address this, we propose SOPE, an algorithm that uses an actor-aligned Off-Policy Policy Evaluation (OPE) signal as an automated early-stopping mechanism to dynamically control the length of offline training phases. By evaluating the critic on a held-out validation split under the current policy's action distribution, SOPE halts gradient updates exactly when out-of-distribution benefits saturate, eliminating the need for manual schedule tuning. 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By evaluating the critic on a held-out validation split under the current policy's action distribution, SOPE halts gradient updates exactly when out-of-distribution benefits saturate, eliminating the need for manual schedule tuning. 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