This subject is so old!
Elsewhere in this forum you can find flight schedules for commercial flights in the southern hemisphere, thorough discussions on the merits of the jetstreams that supposedly push airplanes fast enough to accomodate FE proponents, and so on...
There are even detailed discussions on the voyages of James Clarke Ross, who circumnavigated most of Antartica starting in 1841 and carefully plotted his course long before a Flat Earth Society or a NASA existed, so the lack of a map is not due to a lack of reliable information.
Please do not cry for the lack of a map, do it or accept that you cannot because you are wrong.