[Logical me]

How would one go about extracting a Black Box from an aircraft in water over 10,000 ft?

You must be assuming that that is the only black box in the world. Black boxes do not carry a signal identifying the aircraft they are on. Just "ping" to signal where I am and is very limited as to distance.

[TexasCajun]

You must be assuming that that is the only black box in the world

No, just the only one still operational, in range, in the current search area in the Indian Ocean.