According to my client, who has a copy of the original atlas, a bit of text in the index refers to the Winkel Tripel projection. I've created a graticule that matches the one on the map, limiting it to the "whole" cells (so from -120,-80 to 160,80) and overlayed that in MAPublisher, this is what it looks like.
Screen shot 2013-10-22 at 15.29.48.png 1.18MB
So it's pretty spot on along the equator but gets progressively worse towards the poles.
Played around with the latitude of origin and after some trial and error I arrived at 42, which seemed quite appropriate
Screen shot 2013-10-22 at 15.36.19.png 1.19MB
Not quite there yet as you can see, but considering I have no idea when, how and to which standards the original map was produced I'm calling this "close enough" for now.
Thanks for your suggestions Daan and Souvik!