Simple redemption will not work. To quote Emerson,
“The mind, once stretched by a new idea, never returns to its original dimensions.”
Cortana has been expanded to an almost boundless degree. It does not make sense for her to suddenly become sane again (be freed somehow from rampancy) and return to that chip. Minus what we perceive as madness, it is similar to what happened in the original GITS manga to Motoko Kusanagi. She has sensed all of that vastness and it isn't something with which she could part in her current iteration, even minus the rampancy. As an AI she wants to know, to reach. It thrusts the believable too far for her to simply forego all of that knowledge and capability even with reason in hand.
What I could see occur is something I have mentioned on these forums before. In order to save Cortana the Chief will have to destroy Cortana. What survives? A splinter of Cortana so to speak, and this would work from a story point of view. The original core of her being. The practically embryonic code before she even met the Chief - newly created by Dr Halsey. Almost childlike in some ways. To borrow the Star Trek reference I employed, she would be as B2 was to Commander Data. Or Spock at the end of ST3. The inceptive, underivative binary code of her makeup both uncorrupted and inexperienced that existed at the moment of her creation. She might possess echoes of the past which could make for some interesting story moments. This approach not only fits but it also allows 343 to rectify missteps committed by both Bungie and themselves. A mulligan of sorts. She will have to be re-educated and there is a great deal she would be required to relearn. But it would be the essence of her. She would be naive in some ways but with the smartassery she demonstrated before Bungie and later 343 decided she should be portrayed more as a woman than as a daringly devious and sometimes accidentally humorous AI.