When people refer to ‘sensitive projects’ they nearly always mean dealing with difficult people. Usually, this means individuals who are described by colleagues as, ‘unreasonable’, ‘aggressive’, ‘opinionated’, ‘a refusnik’. There will also undoubtedly be a ‘personality clash’.
Thus, it is not the project that is ‘sensitive’, it is the people involved. Therefore, concentrate on the people issues and don’t waste time on the surface manifestation, which may be some narrow, clinical or technical issue. If you get distracted onto the surface issue you will get bogged down in expert opinion, which will become ever more narrow, leading to a dead end. Insist on working on the people issues and the technical ones will take care of themselves!