Since it doesn't look like your landmass is too large, an equirectangular projection centered at 60 S (instead of the equator like usual) should minimize distortions for you. Heck, even an orthographic projection centered on the center of your landmass would probably be fine for your purposes. So, you could draw your continent in the shape that you want to be, then project that back to equirectangular if needed using something like MMPS.