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This paper investigates rubric-aware, multitask fine-tuning of transformer models for automated grading of introductory C++ programming assignments, with the goal of producing grade predictions that better reflect instructor grading behavior than general-purpose LLMs. Using multi-semester CS1 data, student submissions are paired with numeric scores, letter-grade buckets, and assignment rubrics, then preprocessed into unified sequences for transformer input. A BART encoder-decoder with LoRA adaptation is trained to jointly predict numeric grades and grade buckets, augmented with a distribution-matching term to align predicted and empirical grade distributions, an evaluation dimension often overlooked in prior work. Experiments compare single-task and multitask training, hard one-hot versus fuzzy and boundary-based soft labels, and rubric versus no-rubric conditions, with additional T5 and pairwise-pretrained variants. Results show that multitask BART with boundary-based soft labels and rubric context achieves lower mean absolute error and stronger grade-distribution alignment than single-task, hard-label, or code-only baselines. Fully fine-tuned T5 further improves distributional fidelity, while pairwise pretraining reduces numeric error at the cost of minority-class sensitivity. Collectively, the findings suggest that calibration-aware, rubric-guided training produces more instructor-like grading behavior than accuracy-optimized alternatives.