I would suggest that those looking for the crashed aircraft have a look at the Palomares B52 crash of 1966 when a nuclear weapon was lost in the Mediterranean for over two and a half months despite the full resources of the United States Navy looking for it.The bomb was located but was lost again when it was being recovered and it took a further two weeks to relocate it.
Recovering the recorders from the bottom of the ocean is going to be a very slow and difficult job,assuming that they are ever found.
1966 Palomares B-52 crash - Wikipedia, the free encyclopedia