I wish I could explain how much I agree with you on everything you just said but what it sounds like to me is you need to clean up the registry. Since this is an HP computer, what may be happening is, that due to a corrupt registry file, you may be having problems getting anything HP to install. It's pulling in but in the end when the files are trying to tie together, it is failing (seen a clean install of the OS fix this but I won't go there just yet).
Do you have a preferred registry cleaning software? I know a lot of experts here really like Advanced System Care. I like CCleaner because you can do a system backup within the tool. With this being an HP computer, I am not too comfortable giving instructions on cleaning specific registry keys if one has never done so before. Remember with 3rd party software, user discretion is advised and I'm not responsible for damages. --System Backup and Restore--
If you customize the installation and that fails (assuming you are already trying that before I send my response now), I have some strange luck using HP Install Wizard in these kinds of instances. It is a different executable for installing the printer.
I had this software patch work just today: --Solution Center Update--
I hope I have given what you need to get setup. Oh, don't forget to disable startup services just in case.
Let me know what happens this time.