It must be possible to mod a megaminx to make it. This is how I thought about doing it.
Sand down megaminx to a sphere, should make for a more stable puzzle than simply using the kernel. (Could stop here and paint a globe on it for an interesting puzzle!)
Build up the pieces with sheet material & milliput. Corners should be simple, edges will need a key that runs under the corners. Maybe cast from these pieces if they are good enough.
Should do it!
Lots of work