Using the Doctor as a plot point/objective makes a lot of sense. I like the idea of having to take control of him, only moving by the controlling player (and maybe minis have to stay close to him, or he reverts to wandering randomly, or moving to back to a preset point?). The controllling player can lead him to, and use him to, achieve in game goals - which only the Dr can interact with (and each goal taking multiple turns to achieve). So players would be constantly vying to grab him.
I guess it's a mixture of DWMG and Pulp Alley game mechanisms?