Although it's not always the most fun thing, it's probably "right up there" - when I'm able to be the one who answers my own question. And it turns out that the answer was at least pretty close to staring me in the face almost every day, and the clue was at least partially contained in my original question.
You'll recall that I noted in my original question that some websites will include a Print icon, that allows the current website content to be optimized for printing, but without graphics and ads and other things - that would ordinarily be printed, by just using your browser's Print command. At least one time while using one of these embedded print-friendly website icons, I happened to look at the resulting output - and lo and behold, it indicated that the content had been generated by processing the standard webpage content through another website called - Print Friendly
Turns out the website can also be accessed by end-users to manually generate print friendly output, or output in .pdf format - which you can download (and save) and/or conceivably print later. The Print Friendly interface is about as easy as it can be - as you simply Copy & Paste your website's URL string, and then press Print Preview. The application does a nice job on the output, and even allows the end-user to manually select and delete sections of the output - if for instance you don't want to print any pictures or graphics that may be part of the page content. I've noticed that there are
the oh-so rare instances when Print Friendly is unable to reliably generate the page content and/or sometimes not at all - but those instances are incredibly rare. This application is a winner - try it.