I think you have successfully illustrated the failure of "global south" as a replacement term.
I'm not against replacing "third world", but something with the word "south" is ambiguous and counterintuitive.
I'm not against replacing "third world", but something with the word "south" is ambiguous and counterintuitive.
'Southern hemisphere' is fine though I think? And I assume that's what was meant.
Your conclusion is my point.