Granted I was romancing Zarad when I freed her, but I managed to do so without chosing any of the "work towards my interest choices" or spending influence on Hise/Corval.
Feels like nation approval + making the right convo choices with the delegates during week six is king for getting what you want at the negotiations - if you have the near max approval levels that lets you volunteer three choices at each talk you should be able to get her free and sue for some sort of peace with everyone without even spending any influence .