I think I now have everything fixed, but let me give you the background.
First, I regularly use CCleaner, and in fact I used it a couple of weeks ago to clean up the Registry - before all this started. I don't believe the startup services ever had anything to do with it; I didn't disable them this round.
Today after starting my system I began systematically to go through the solution you linked, although I skipped the .NET update because I did that yesterday. When I first ran the installer, I carefully unchecked everything except the drivers, and clicked OK, and then accepted the conditions - and the unmentionable installer proceeded to install everything, despite what I told it to do. I forgive it, because it ran a clean install. HP Solution Center is reinstalled and working, and incredibly it has saved all my custom configurations. I appreciate the link to the Solution Center update but after this I am not going to touch it.
Frankly, I blame the whole mess on the undocumented dependency on .NET 4.5. I hope someone in HP will take a moment to put that on the System Requirements page for the driver installer, to save someone less skilled at troubleshooting than I am the mess I've just been through.
Now I just have to clean up my startup files and I think I can get some actual work done. Thank you again for your patience and your recommendations.
hedera