Thanks for all the responses. Before I saw them, I did what I said I would try above and that was to just do an upgrade install of 7 right over the vista partition. That worked out OK so the problem is solved for the time being.
But you guys got me wondering what would have happened if I had disconnected the external drive and tried again to do a clean install. Btw, of course the USB flash drive was properly made bootable and the files (not the actual ISO itself) from the Windows 7 ISO were copied over to the bootable flash drive, so that wasn't the source of the problem.
I get the sense that perhaps if I had tried disconnecting the external hard drive from the system, it might have allowed me to clean install Windows 7. But since this is just a temporary installation on a "borrowed" rig while my main machine is in the shop getting its system board replaced under warranty, I'm just happy to have Windows 7 installed and working, even if it isn't a clean install.
(OT: While this is a nice powerful machine, it sure is not easy getting used to the keyboard and ergonomics of an HP after coming from years of using Thinkpads. Kind of nice to have 1 GB of dedicated video ram, however.)