Well, I tried to work through the recommended solution.
First, doing the install in another user is no good. It didn't work either.
I did check .NET and discovered that I was backleveled - I had Framework 4 and the latest version is 4.5. After installing that, and running the seven Windows updates, I tried the rest of the script.
Couldn't run step 4, there was no bpd_scan folder and no bpd_scan_carrier executable.
Ran scan.msi, no apparent effect.
I could now run the install software without getting the "missing disk" message in the first few minutes. Until now I had never got far enough into the process to see the license and EULA page; and the only time I did see it, when I clicked on the "select files" link I got a blank window. I tried to install only the drivers; but I got confused among the windows and unintentionally ran an install for everything, including things I don't want on my system like Photosmart Essentials. This said that it installed HP Solution Center; but during the install of HP Customer Participation (about which I don't give a rat's patoot) the installer hung and I had to kill it. After which I still can't bring up HP Solution Center. So I now have to start all over and run the uninstaller.
Apart from still being annoyed about this crummy software, I am appalled that the installer should have such a strong dependency on .NET 4.5 which is not mentioned anywhere on the System Requirements page! I know it isn't because I LOOKED at that page and it was blank.