This paper presents a solution to address wear and tear of Run-of-River (RoR) Hydropower Plants (HPPs) providing enhanced Frequency Containment Reserve (FCR). In this respect, the study proposes the integration of a Battery Energy Storage System (BESS) with RoR HPPs controlled by a double-layer Model Predictive Control (MPC). The upper layer MPC acts as a state of energy manager for the BESS, employing a forecast of the required regulating energy for the next hour. The lower-layer MPC optimally allocates the power set-point between the turbine and the BESS. Reduced-scale experiments are performed on a one-of-a-kind testing platform to validate the proposed MPC-based control considering a comparison with different control strategies and different BESS sizes. The results demonstrate superior performance of the proposed framework, compared to simpler techniques like dead-band control or to the standalone RoR scenario, leading to improved FCR provision, reduced servomechanism stress, and extended hydropower asset lifespan.