Well ... My wife just happened to have a DVD player in her car from an even she was working ... So I decided to give the update another go. SUCCESS!!!
The DVD player I was using that did not successfully update was a Sony DVP SR200P. The one from my wife's car was a Phillips DVP 5992/37. For what it's worth, I did my initial update on my Classics with a Harmon Kardon DVD player.
I don't know if it is newer, since I am not sure who old the Phillips one is. But it definitely is not fancier.
I think I just paid about $40 for it, because I just needed to replace a broken one. I'm shopping around for a Blu-Ray and didn't see the need to spend that much on a standard DVD player.