In my limited experience of your type of situation; I think you need a better diagnosis.
Unless you know specifically that it’s a (pre)Cochlea malfunction, a CI might not be the answer. If the discrimination issue is a retro-cochlea function, putting a CI in the system is unlikely to resolve the speech-in-noise issue; but will still give you all the surgical risk AND a huge rehabilitation issue to deal with alongside.
Also any naturally acquired stereo directional processing that you already have will be lost as the CI installation will introduce a temporal shift to the sound on one side.
I’d argue there’s a lot of methods to try first - even hearing aids with a near field partner mic would seem a better solution.