All of this is true, which is why you can only go episodes they appeared in, since there are so many unknown factors.Except that Amy and Rory are no longer traveling with the Doctor at that point. Their appearance in "The Doctor, the Widow, the Missing Oxford Comma, and the Wardrobe" is the equivalent of the Doctor visiting Martha in the fourth season or any of the appearances at the end of "The End of Time Part Two" -- they're guest stars, not ongoing characters. It's possible, even likely, that they have spent more time with the Doctor than Rose did (certainly, there's a lot we haven't seen, if only to account for the time that Amy's pregnancy would have taken), but Rose likely spent more consecutive time traveling with the Doctor.Incorrect, did you not watch it all the way until the end? The Widow insists the Doctor should go home for Christmas, and he shows up at Ammy and Rory's for Christmas Dinner.Amy didn't get the 2011 Christmas special, though - surely that interrupts "continuously serving", leaving her tied with Rose?![]()
Amy and Rory are odd companions in the sense that the Doctor keeps ditching them for extended periods of time, only to come back into their lives for a new round of adventures. There's a multi-month gap between seasons five and six where they've left the TARDIS (but expect the Doctor to return at some point), and then there's another gap of unspecified time between "A Good Man Goes to War" and "Let's Kill Hitler" where, again, they've left the TARDIS and, again, expect the Doctor to return for them.
It's like that Amy and Rory have traveled with the Doctor for longer than Rose (certainly, there's more time than we saw on screen, if only to account for the time Amy's pregnancy would have occupied), but Rose likely traveled with the Doctor for more consecutive time.
Once a Companion, I think a return appearance, still counts as them being a Companion, even if they don't step foot in the TARDIS in that episode, IMHO, of course
I consider Sarahjane a Companion in her NuWho appearances, due to being Tom Baker and Jon Pertwee's Companion.