In the image above, the black shape was exported from IcoMoon, and the blue shape is the original SVG.
As you can see the quality of the export is pretty shocking, with jagged edges on pretty much all curved surfaces.
It's worth pointing out that the one <circle> object in the SVG exported correctly, and this only appears to be an issue with paths. (Possibly complexity limits?)
I have sent the problem SVG to Keith.
Thanks for your help!