I think I may have resolved this problem. Here's what I did:
1. On the 2003 Server, I installed the Universal PCL 6 Driver on each relevant printer instance. The installation process was smooth and everything went as could be expected - no hanging, no strange error messages, etc.
2. On the Windows 7 computer I deleted all the network printers. Next I connected to this printer using the following method (written from memory, may not be exact): Add Printer Wizard > Local Printer > Create a New Port > Local Port > \\servername\ExactPrinterShareName > Follow Prompts to Install The Correct Driver From Disk After installing the printer using this method I simply left it this way.
3. On the Windows XP machines I just deleted the printer instances, browsed to the server that has the shared printers using \\ServerName, and then right-clicked on each printer and clicked on Connect. I didn't have to do this on all of the XP machines. I only did this on the one where the user was reporting a problem.