Mitchell: "The first thing I ever heard from upperclassmen was, ''Watch out for Lieutenant Kirk. In his class, you either think or sink.''
Dr. Dehner: "Gary told me you've (Kirk) been friends since he joined the service, that you asked for him aboard your first command."
Kirk: "Our task-- transport down a man I've known for 15 years, and if we're successful, maroon him there."
Mitchell: "My friend, James Kirk. Remember those rodent things on Dimorus? The poisoned darts they threw? I took one meant for you. And almost died."
It seems like the heroic life saving was during a mission (shades of Spock in The Apple).
I'm not saying it would be impossible to have Mitchell in the film, it would just need to be done right or it's going to either a) violate the established timeline or b) feel really forced.
Thanks to Ron Salon for the signature banner!