Bryan,
That's what we all have been trying to tell you here.
The drivers directly from your old software or directly from HP are no longer working like you finally found out.
You needed the drivers from the Snow Leopard disk or download the new ones from Apple like you finally did. The drivers you downloaded are the same ones on the Snow Leopard disk as stated on the page you linked to.
http://support.apple.com/kb/DL907
About HP Printer Drivers for Mac OS X v10.6
This download includes HP printing software that shipped with Mac OS X v10.6 (Snow Leopard).
Glad you finally got it working.