I've sometimes used a Firefox extension that copies HTML as HTML into the Notetab editor, and using Notetab's built-in feature to strip HTML but retain URLs, though still have to add the URL of the page itself as a separate operation.
I have thought of doing this but would really like a more simple solution. I do like Notetab, but don't have a license for the pro version, and feel limited by the non-unlimited undo of notetab light. I like Notepad++ and Editor<sup>2</sup>. I'm sure there are many notepad replacements and other programs that have HTML stripping functions where I could do as you described, this may be my only option if I can't get something else to work.
html2text: you might also like Nir Sofer's freeware HTMLAsText, which can also be run from the command line if required.
I did notice this program in my searching. It appears the HTML must be saved as a file before this can be used. Again, a good program, but I would really like to do this a with basic copy and paste action or something similar. Perhaps I could write a script that would temporarily save the HTML snippet as a file, process it with HTMLAsText, then copy the converted text ready to be pasted? I don't know if I can do this with your other suggestion, Clipboard Help+Spell. I'll have to look into it. From the surface it doesn't look like it can easily be done.