Turns out the wall of the casing is a tad too thick in order to fit the neopixel ring I just received. 

And I don't have access to a lathe, so I shaved off the 1mm excess with a coarse round file after mounting the casing on a drill. I clamped the portable drill on the bench for that and such filed the inside for 30-40mm.

I then finished the surface with sandpaper.