If I was them, I would try to move the whole asteroid. Maybe Amun is too big, but there will be smaller ones. Whith a little billiard playing with gravity, they could be "smoothly crashed" into the Moon, or even some deserted Earth location. Maybe ideal result would be placing it in not-so-low Earth orbit and make the extracted materials go spiraling down to the surface.
Disclaimer: I haven't the faintest idea of the amount of energy needed to move celestial bodies, but I guess it could be made so the first targets will be small ones and using the resources obtained from them, create stronger and stronger infrastructure to capture bigger ones.
EDIT: Archimedes already said it. To move worlds they first need a big enough lever and a place to put it.
"Mining the Moon" as in digging holes there is not the same as picking up the pieces of a crashed metal mountain. Anyway, forget that. Put the asteroid in Earth's orbit and work from there. What about the value of a new moon that could be used as a gigantic station?
Disclaimer: I haven't the faintest idea of the amount of energy needed to move celestial bodies, but I guess it could be made so the first targets will be small ones and using the resources obtained from them, create stronger and stronger infrastructure to capture bigger ones.
EDIT: Archimedes already said it. To move worlds they first need a big enough lever and a place to put it.