The tip couldn't have broken off because I did get the drive to start up a few times before and the exact same sound was there before it started up.
My two new drives are arriving today, so first off I'll replace the logic board and see if that makes any difference. Then I'm supposed to get a 2.5 to 3.5 converter cable later in the week, so that I can try connecting the drive to a desktop before I go into surgery. If that doesn't work, I'll start ripping the guts of the new drives to see how much trauma they can take on. If all goes well, I'll move on to the actual patient, who by the way had been frozen for its third day in a row now.
I'll keep you posted on the progress.