Re: "they need to have a clear business case"
I'm afraid interfacing projects would take ages to be completed. This would only might work in greenfield scenario, when you don't need to retrain users to use these new tools.
But S/4HANA greenfield implementation is also super easy now. My company's record time for implementing is 30MD for FI, SD, MM and PP (each) per country - excluding time on minor additional developments in outputs an reports which took totally 10 MD.