Okay, I used MeshesIntersect(), but it still seems a little buggy.
That is odd - I have always found it robust (the only thing to take care to ensure is that the meshes in question are not flat, which they aren't here). There's no collision response with the command - meshes will just drift through each other, but for Asteroids this is typically okay because as soon as you hit one you're dead!
Depending what you think of the code I posted above, you might not be interested in MeshesIntersect() any more; but if you want me to cast my eye over the MeshesIntersect code you found troublesome then post away.