" major land masses that would FIT INSIDE Africa, so huge is it (the United States; India; all of Europe; Australia; many others - none of them overlapping), "

sorry...IF you saw such, it is just wrong...all those countries will not fit into Africa...perhaps there was a mis-understanding. Africa is about 4000x4000 miles, with a bite out of the lower left quadrant...the US is 3000x2000 or so...you could cram Europe in,...and parts of Australia...but India gets left out...The Peters Map is terribly mis-leading...I need to read more about it and how it is viewed by cartogrophers, but Africa, though large is not THAT large...

here is a page of map resources