Good Day aparente001,
I too had the same problem as you are referring to, so I know exactly what you are talking about. So to answer your question:
Do I need to go through each of those cases and provide detailed css changes, or is there a more elegant way?
You will have to go through creating a Child Theme (as you did already) of your current Twenty Fourteen and make the changes yourself as you were scared of.
Depending on the needs of your website, you probably will have to go through each cases that will be needed by your website, the “easy” way is to use a browser (I use firefox and Mac and it worked like a charm) and just resize it at the current case you are working on and you will see the modification right away (You can even see the “mobile” version by resizing it to the smallest. (I will be using a Mobile “theme” plugin because the mobile version of Twenty Fourteen is not the best).
My website doesn’t need all the cases so it was fairly easy, it’s a travel blog and I know that most of my friends that follow me will read it on their computer. But it’s true that for a business or a wider range of audience website, Twenty Fourteen (even though it has an interesting look) is not the greatest.
That’s exactly how I had to do it (you can see my results on Sly The Traveller).
It was made rather “quickly” so I know that mine is not even perfect, but as I said for my readers it doesn’t need to be.