Wellllll... I didn't do enough trouble-shooting before buying that drive... I installed it this morning and had the same symptoms! I did some tests using my other external drive and I interpreted the results as indicating that the original drive was bad. I think that the intermittent nature of the problem and the varying symptoms fooled me...
MORE time spent trouble-shooting and it would appear that the Firewire ports are dying, which likely means that a logic board replacement is in order.
Thankfully it is still under the 1-year warranty period, but I had to go ahead and purchase AppleCare in order to get telephone assistance from Apple.
I hope that mine (3rd generation) isn't one of those "problem" G5 iMacs that will require multiple logic board replacements. The fellow in the shop at the local Apple dealer told me that they see "lots" of sick G5 iMacs.
Time to start backing-up everything via USB 2.0...