I don't think Hagrid was ever a father figure. Dumbledore, Sirius, and Lupin sure, but Hagrid was more of a friend and guardian than any kind of paternal figure.
Luna couldn't have befriended the trio in the first year, as she's a year younger than them.
Other than those two statements, I agree. Remus is easily the most responsible of Harry's father figures and doesn't get as much credit as he deserves.
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