One last thing (sorry, this morning I was a bit in hurry).
In approaching difficult clients/stakeholders, I found very useful to explain in detail every choices that has been made, possibly quoting studies or researches.
People usually tend to trust more what is written rather than words, so if you give them something they could check (even if usually no one does, and it’s a pity) they feel more comfortable in trying new approaches (the expert say so, and there is a paper about that! …power of an opinion leader…)
Engaging them in the process, showing how things change in better as Dopamino suggested is a great point, and if you succeed in doing it, it will be easier in the further steps (you gained their trust! )
P.s. Thanks @jacquidow (I’ ve been lazy lately…)