Here's how I solved this problem:
True MacGyver style...floss pick, rubber band, super glue.
I had a floss pick, I used a razor blade to cut out an L shape in the plastic handle of the floss pick. I stuck that back inside of the connector (if you cut it right/small enough, it will kind of "fall" into place back there, and actually be pretty damn hard to get out). This will help to reduce the "play" inside the connector and help the pins make better contact.
Next, I found a rubber band. I tied several loops around the cable, then strung it around the hard drive.
By now, the cable is somewhat solid and making good contact. So lastly, add a dab of super glue to adhere the connector to the drive itself. Make sure to squeeze and hold it really tight and keep doing so until the glue dries. By the end, it should be pretty good construction.
Here's a photo: http://img.photobucket.com/albums/v601/zoned019/IMAG0042_zpsc1683ef9.jpg
It's been working wonderfully :-D