arXiv:2610.29588v1 Announce Type: new Abstract: Mobile edge services can combine local computation with satellite and cellular access to deliver time-sensitive results in areas with intermittent terrestrial coverage. Meeting their deadlines and quality requirements calls for joint computation and transmission scheduling that accounts for task dependencies, changing link capacity, and shared resource budgets. However, optimizing resource allocations or tuning parameters within a fixed policy structure offers limited scope to correct failures rooted in the scheduling logic. We propose SatCraft, a framework in which a large language model (LLM) agent uses execution feedback to revise the code of joint scheduling policies. Each revision undergoes policy checks and complete-run evaluation to assess its validity, runtime, and effects on service completion. Because policy performance varies with access conditions, SatCraft retains valid alternatives in a policy library and selects one for each episode using initial access observations and the known resource configuration. Experiments using Starlink and cellular measurement data show that SatCraft improves cumulative completed-service value by 3.61%-16.89% over baselines, including recent state-of-the-art scheduling methods ADPRL, EdgeOPT, and TF-DDRL. It achieves the highest completed-service value in all four resource profiles and averages 25.02 ms per scheduling call. These results demonstrate how LLM-guided policy optimization can improve complete service delivery under the computing, communication, and quality constraints of satellite-cellular networks.