Your Neo/Mwu theory that he will pilot Freedom was wishful thinking.
Shinn gave Stellar back to EAF because he could do nothing to help her, and she was dieing. He gave her back because he was not a scientist, did not have the necessary equipment to help her, and he wanted her to live because he loved her [or at least had a strong crush on her]. I don't think Shinn would go through all this trouble just "to pass the buck and not feel responsible" if it could mean getting killed himself by disobeying orders.