This study focuses on optimizing solid oxide electrolysis cell (SOEC) systems for efficient and durable long-term hydrogen (H2) production. While the elevated operating temperatures of SOECs offer advantages in terms of efficiency, they also lead to chemical degradation, which shortens cell lifespan. To address this challenge, dynamic degradation models are coupled with a steady-state, two-dimensional, non-isothermal SOEC model and steady-state auxiliary balance of plant equipment models, within the IDAES modeling and optimization framework. A quasi-steady state approach is presented to reduce model size and computational complexity. Long-term dynamic simulations at constant H2 production rate illustrate the thermal effects of chemical degradation. Dynamic optimization is used to minimize the lifetime cost of H2 production, accounting for SOEC replacement, operating, and energy expenses. Several optimized operating profiles are compared by calculating the Levelized Cost of Hydrogen (LCOH).