Math With Bad Drawing has some images that approach an info-graph (and in general is just a great website for math education), for example:
There are some good geometry ones, especially around old compass and straight-edge constructions but that ...
"Kids usually struggle with every one of these concepts, let alone all of them together. It is difficult to get the whole picture and all the moving parts. So this place (proof) seems like a good place to show all of this in action."
I'm afraid there is no "complete picture" of all the facets of logic and proof that you mention, interrelating in one ...
Maybe you can do President Garfield's proof and combine it with a history lesson.
page 161 of the New-England Journal of Education, April 1, 1876 (image from Google Books)
Note: M. C. = Member of Congress.
I am grateful to Mark Conger for finding a video of this presentation and getting the University of Michigan to digitize it. It isn't produced in the style of math youtube content, because that was presumably not the goal of QED TV, which I do not know the history of. But it is found! I finally have a link to the video! Here it is:
The video spends a lot of ...
This was in my math folder, I don't know its source.
It was shown as 'not needing any further explanation', but of course, for lower level students, I connect the 3 points on the circle's perimeter to form the larger right triangle and remind them of the ratios formed by dropping an altitude (line b).