Bored last night, and inspired by someone else's recent efforts to do the same with Bruce Wayne, I combined all the faces of the doctors in a face-mergy thing to see what the 'essential' doctor might look like. Turns out, he looks kind of like Liam Neeson:
I then roughly pasted the face on a a suitable head:
And that was about it.
If I get some more time/inclination I might try polishing it up a bit, altering the face to better represent the shape of the composite, but the image is so low quality it may not be worth really investing in it.