Update to everyone in this thread: the 2 new 1TB hard drives I received from AppleCare also failed identically to the 2 original drives I had. The common thread -- they are all Hitachi drives.
Now I had happened to buy 2 new Western Digital Caviar drives, which arrived at the same time, and I installed OS X on those and tested those. Here's the upshot: the Western Digital drives worked perfectly, and I had no problems with either of those drives, in any of the 4 drive bays in my Mac Pro. However, the Hitachi drives from Apple all failed in all 4 of the drive bays.
AppleCare has determined the difference between the Western Digital and Hitachi drive specs to be the amperage required -- the Western Digital's are energy efficient, and run on lower amperage, while the HItachi's are not, and run on higher amperage. The working theory at the present is this: we've ruled out drive bays or the main board as problems, and given the power difference, the theory is that this has to do with a power supply issue. This has relevance to both internal and external hard drives, as externals that might pull power from the main box might be suffering from lack of power from a weak or dying power supply.
If anyone is having the problem with internal hard drives, particularly Hitachi's from Apple, AppleCare asked me to ask you to post your serial number to your Mac so that they can tie another case to this issue. They said that would really help solve the problem. If you'd rather do this offline, you can contact me at brado77@me.com.
Thanks...