The good news is that the people at Gillware, Inc. were able to recover data from the hard drive.
The bad news is that the tech says that this was a "rough extraction." Bad enough that they charged me only half of what they normally would. The directories were intact, but he says that there are a number of files that, though they show up on the directory, are corrupted very badly.
The new external hard drive with the recovered data on it is on its way. They estimate delivery by the 7th. I'll update then with a damage report.