Yeah, I figured that Hogwarts would have some kind of safety backup plan in case if students are to have unfit guardians, so they'd go to their Head of House and unless if that causes any issues, then that's just the default placement. Although I do think Minerva would be a good fit, she likely recognizes that Severus seems to care about the boy and he's younger and more capable of emphathizing with his situation. Also, she does think it would be a good way for him to heal from his own... wounds about Potter and the Marauders and help him see that Harry isn't them and that those years are over.

Thank you! I really appreciate the feedback. I'm glad you think it's in character. :D