After many hours of attempting to get the Qosmio to recognize the Dynadock U3.0, I finally tried using my Toshiba netbook. Alas, it installed fine.
Then I tried the Qosmio again and it recognized the Dynadock and it is now functional.
It seems that the Dynadock needed to download some firmware before it could be recognized by the Qosmio, but it could not update itself until it was connected. Quite the conundrum.