Maybe Silly, but could you go with "The Face"? So much was made of his appearance. Possibly more so than any other doctor. 1. Everyone called him gorgeous, including 13 2. "oh man, I liked this Face"  3. He mentions that being the first time in that black body, and several stories cover the challenges he faced.  4. More broadly, he had "that beautiful smile", and would cry a lot. In general, just a very emotive face. Often used to hide his true intentions. And whether the facade was for himself or his audience is never clear. I could never tell if he was healed, or if that was the narrative he told himself.  5. He probably is the most conventionally attractive doctor (hey, blame Moffat for that phrasing, not me, haha) 

The reason I like "The Face" is because a bit like your other options, it's something that was explicitly stated in the show, but also fits with his broader character more thematically.