The strange things is, if I export the game using a slightly older version of C2, my game works on Cocoon. Version 152.2... doesn't work at all!
This leads me to think it's Construct with the problem, rather than Cocoon on this occasion, but then again I'm ignorant to the intricacies.
Have Ludei simply not updated the exporter? Using the launcher, I just get "Unzipping" and then it just sits there doing nothing. Again, this is only games from 152.2.