You know, it's funny how things work. I downloaded the source code from SourceForge, and put in the support files for my printer and it worked well. Then I came back here to report what I had done and saw Paul's new build, done for my request.
Well, I went to another machine, and installed the new HPLIP over my existing eCups installation. I also updated Alex Taylor's print manager because I'm tired of operating the one in the Dutch Language. Well it worked perfectly. Thanks, Paul. And this was a real dummy install. I just followed along in the GUI, found my printer, and after installation tried to print from Firefox. In a couple of seconds, the printer spat out a good print of my webpage.
Notes:
Paul's new build of HPLIP is meant to be unzipped from the root. It will overwrite \hplip and \cups with the updated files.
There are so many supported printers, that it is hard to find the right one.
I plugged the printer into my wired network. I assigned it a static IP. eCups found it, so I did not have to configure the network.
To install the printer, I used Alex Taylor's "Install printer". I never saw any eCups screen. It just worked.