Circumnavigation by Carnegie in 1916 took 4 months but was well north of 60S.

You can see that the route of the Carnegie never goes higher than 60S latitude. You can see for yourself that there are significant "short cuts' being taken by the ship as seen in the pointed peaks of the dark line in the map below. On an azimuthal flat earth projection, those will be clearly seen as shortening the trip considerably. 

Notice that Antarctica is not completely outlined below. Note too that above 60S, the distance on an azimuthal projection increases considerably. It's quite concievable that if the short-cut routes of the Carnegie took 4 months-- that a non-short-cut-above-60S route (around 75S) -- would have taken much longer. My inaccurate sketch of that projection doesn't quite make that clear but you can at least see the problem we're faced with. More accurate maps can certainly be made... I'm just proposing a direction of research. 

Here's are links to stories about the Carnegie's voyages, including this Antarctica one.

Ocean Magnetic Survey Expeditions: The Carnegie

https://library.gl.ciw.edu/ocean/carnegie/main.html

J.P. Ault: A Scientist at Sea, Voyages: Antarctic Circumnavigation

http://publicationsonline.carnegiescience.edu/legacy/exhibits/ault_exhibition/antarctica.html

I created the following map quickly in 5 minutes by eyeballing alone. It's not accurate but it's a starting point. You can see there's a big difference between the yellow line, the voyage as close as I could get it in 5 minutes, vs. that orange line which goes along Antarctica's coast. I guess we would have to capture the ship's logs and their latitude and longitude estimates-- and how they got those numbers-- a century ago. It's typical of many if not all of the circumnavigations of Antarctica I've seen involve latitudes that are too high for satisfying my curiosity about the true distance around Antarctica-- and the Carnegie is just another one-- albeit a bit more interesting than, say, the Vendee Races or individuals doing yacht trips around the southern oceans.