the next Doctor (Capaldi) being a physically older regeneration makes complete sense: The Doctor's forgiven himself. He doesn't have to run away from adulthood any more. He can grow up now.

Totally agreed; see above! I didn't think of it in terms of forgiveness, but it does make sense of Capaldi's age—I don't mean that it needed defending in the first place, but rather than just being an incidental fact, it is now thematically resonant and moving. That is an exceedingly neat trick.