I just thought of a major point against Kitty being the time traveller, if they go back into their own body. Assuming Kitty is the same age as Ellen Page, or at least close to it, she would have no body to go back into. Ellen Page was born in 1987.
Well, that's an easily ignorable feature of X-Men time travel. Just have her go back without entering her old body.
My hope is that it is not Wolverine who goes back for two reasons. One, he has his own movies where he's the star, so he doesn't need to be the star of this one. And, two, he has a pretty famous death scene in the comics and it would be nice to see that on the big screen.
I could easily see him dying in the future and then he gets seen in the past and recruited to help. The only issues are ones of him joining the X-Men too early, but that's relatively fixable since he hasn't lost his memory yet (assuming that everything isn't getting rewritten anyway).