[Python] How to build a correct cartopy feature around the south pole?

I want to build a cartopy feature for Antartica in palaeo geography. I have the lon/lat of the coastline.

I cant find a way to have a nice plot in any projection.

Here is an example that plot a simple circle (filled) around the south pole. It gives an ugly result in some projection.

Is there a trick to make this work?

import numpy as np
import matplotlib.pyplot as plt, matplotlib as mpl
import cartopy.crs as ccrs, cartopy
import shapely as shp

# Defines a circle around Antartica
nn = 20
lon_coast = np.linspace (start=-180, stop=180, num=nn)
lat_coast = np.ones (nn)*(-70)
coord_coast = np.stack ( [lon_coast, lat_coast] ).T

coord_coast = np.vstack ( [coord_coast, np.array([np.nan, np.nan])])

# Build the cartopy feature for the circle
coast_shp = shp.Polygon (coord_coast)
coast_feat = cartopy.feature.ShapelyFeature (coast_shp, ccrs.PlateCarree (central_longitude=0), facecolor='green')

# Plot the circle with various projections
fig = plt.figure(figsize=(12,8) )

def my_fig (idx, proj) :
pos=230+idx
ax = fig.add_subplot (pos, projection=proj)
ax.add_feature (coast_feat, facecolor='green', edgecolor='red')
ax.coastlines ()
ax.gridlines ()

my_fig (1, ccrs.PlateCarree ())
my_fig (2, ccrs.Orthographic (central_latitude=-90))
my_fig (3, ccrs.PlateCarree (central_longitude=180))
my_fig (4, ccrs.Robinson (central_longitude=0))
my_fig (5, ccrs.Robinson (central_longitude=0))
#my_fig (6, ccrs.Stereographic(central_latitude=-90))

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