The integration of Artificial Intelligence (AI) in education requires scalable and efficient frameworks that balance performance, adaptability, and cost. This paper addresses these needs by proposing a shared backbone model architecture enhanced with lightweight LoRA adapters for task-specific fine-tuning, targeting the automated scoring of student responses across 27 mutually exclusive tasks. By achieving competitive performance (average QWK of 0.848 compared to 0.888 for fully fine-tuned models) while reducing GPU memory consumption by 60% and inference latency by 40%, the framework demonstrates significant efficiency gains. This approach aligns with the workshops' focus on improving language models for educational tasks, creating responsible innovations for cost-sensitive deployment, and supporting educators by streamlining assessment workflows. The findings underscore the potential of scalable AI to enhance learning outcomes while maintaining fairness and transparency in automated scoring systems.