The primary purpose of my posting was for sharing my experience. I have seen lots of free advice on the internet. Wading through anecdotes, subjective experiences, and those experts trying to get you to buy equipment via their websites can be a waste of time.
If someone else's results don't agree with mine, it hardly matters. It is my camera, my technique, my results.
The point that I am making and that I believe is valid is that until you test your own equipment you won't know what works and doesn't work. I am recommending taking a baseline and under same conditions adjust the variables. In my case, what was true on a tripod with a fixed target has been validated in the field.
I was not at all happy with the results of shooting my telephoto wide open. My style is about sharp focus.
I was very happy with use of teleconvertors. Image quality of my subject was better than without it. The TC downside is loss of light and some autofocus hunting. I don't use the 1.4TC much because results are better with 1.7TC, ie, why bother with the 1.4?
I don't think my findings were a fluke, it was just my equipment.
You can read on line when diffraction (or any other word we come up with for image blurring) becomes a factor, or you can test it. In my case it was at F16 for a D800 E, with 300 2.8, with and without teleconvertors.