Designing therapeutic messenger RNA (mRNA) requires creating full-length transcripts that carefully balance stability, translation efficiency, and immune safety. To address this challenge, we propose ProMORNA, a multi-objective generation framework that produces complete mRNA transcripts \textit{de novo} directly from a target protein sequence. Our approach begins by training a BART-style encoder-decoder model on over 6 million natural protein-mRNA pairs. We then introduce Multi-Objective Group Relative Policy Optimization (MO-GRPO) to simultaneously optimize for various biological objectives in a unified way. As a case study, we evaluated ProMORNA on the widely used firefly luciferase target, excluding it from both our supervised training data and the prompt pool. The results indicate that ProMORNA improves the \textit{in silico} Pareto frontier for predicted half-life and translation efficiency relative to standard supervised baselines. Additionally, it achieves higher predicted functional scores than a state-of-the-art baseline under the same evaluation pipeline. These computational findings demonstrate the feasibility of using multi-objective reinforcement learning for full-length mRNA design on unseen targets.