Cartopy incorrectly filling outside of Shapely polygon

The Shapely polygon listed below as "mywkt" plots incorrectly in Cartopy; it fills the outside rather than the inside, despite being a valid polygon. In GIS software it plots correctly. The issue is occurring in many projections tested, including the one below. How can I correct it to fill the inside, as would be expected?

import matplotlib.pyplot as plt
import cartopy.crs as ccrs
from cartopy.feature import ShapelyFeature
import shapely
import shapely.wkt as wkt

# Main plot setup, issue occurs regardless of projection used.
fig = plt.figure(figsize=[5, 5])
crs = ccrs.NearsidePerspective(central_longitude=-100, central_latitude=65, satellite_height=6200000)
ax = fig.add_subplot(1, 1, 1, projection=crs)

# Build and plot the polygon, valid
mywkt = "POLYGON ((-66.64127406774401 63.2679483443407, -66.48652697503979 63.1988718046901, -66.4817891045834 63.1004449790526, -66.379143168922 63.0115892305586, -66.1973803825985 62.9848443902565, -66.0559008189676 62.9537393506905, -65.97118398525259 62.9850694644843, -65.850509788396 62.9360773051236, -65.69642646101229 62.9192773820456, -65.6182098640938 62.8587266887857, -65.473922680887 62.8270608886491, -65.3890303678572 62.8197557451316, -65.31233201541011 62.7191354685271, -65.25006848777041 62.6268846390149, -65.12107061571631 62.5688402034127, -64.96662902810711 62.6103134144326, -64.52292746513029 60.3009837190234, -64.678588195289 60.3290634023542, -64.7726142595404 60.3596734442741, -64.8751520004644 60.2840499669325, -64.9515074450125 60.2243558221635, -65.0198404413832 60.1228099129471, -65.095375384966 60.0444670754952, -65.1483835964257 59.944148956709, -65.2920146315699 59.8405379513654, -65.453168021487 59.7919610620534, -65.47048148623151 59.6270483926692, 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-66.5590520172367 63.0848581227043, -66.5560689390303 63.2054750444379, -66.64127406774401 63.2679483443407))"
p = shapely.geometry.Polygon(wkt.loads(mywkt))
print(p.is_valid)
shape_feature = ShapelyFeature([p], ccrs.Geodetic(), edgecolor='black', facecolor="red")
ax.add_feature(shape_feature)
plt.show()

The polygon does not have ccw sequence. To get it right, you need to reverse the sequence. Here is the relevant code that does the trick for you.

# Your code is OK up to this line:
p = shapely.geometry.Polygon(wkt.loads(mywkt))

# Add these lines to reverse vertices sequence
px = p.exterior
if px.is_ccw==False:
    px.coords = list(px.coords)[::-1]

# Continue your remaining code.

Update (thanks to the comment by mintem)

My original code above is now broken. Here is the update given as a full working code and output plot:

import matplotlib.pyplot as plt
import cartopy.crs as ccrs
from cartopy.feature import ShapelyFeature
import shapely
import shapely.wkt as wkt

# Main plot setup, issue occurs regardless of projection used.
fig = plt.figure(figsize=[5, 5])
crs = ccrs.NearsidePerspective(central_longitude=-100, central_latitude=65, satellite_height=6200000)
ax = fig.add_subplot(1, 1, 1, projection=crs)

# Build and plot the polygon, valid
mywkt = "POLYGON ((-66.64127406774401 63.2679483443407, -66.48652697503979 63.1988718046901, -66.4817891045834 63.1004449790526, -66.379143168922 63.0115892305586, -66.1973803825985 62.9848443902565, -66.0559008189676 62.9537393506905, -65.97118398525259 62.9850694644843, -65.850509788396 62.9360773051236, -65.69642646101229 62.9192773820456, -65.6182098640938 62.8587266887857, -65.473922680887 62.8270608886491, -65.3890303678572 62.8197557451316, -65.31233201541011 62.7191354685271, -65.25006848777041 62.6268846390149, -65.12107061571631 62.5688402034127, -64.96662902810711 62.6103134144326, -64.52292746513029 60.3009837190234, -64.678588195289 60.3290634023542, -64.7726142595404 60.3596734442741, -64.8751520004644 60.2840499669325, -64.9515074450125 60.2243558221635, -65.0198404413832 60.1228099129471, -65.095375384966 60.0444670754952, -65.1483835964257 59.944148956709, -65.2920146315699 59.8405379513654, -65.453168021487 59.7919610620534, -65.47048148623151 59.6270483926692, 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-66.5590520172367 63.0848581227043, -66.5560689390303 63.2054750444379, -66.64127406774401 63.2679483443407))"
p = shapely.geometry.Polygon(wkt.loads(mywkt))
print(p.is_valid)  #true

# Add these lines to reverse vertices sequence
px = p.exterior
if px.is_ccw==False:
    #px.coords = list(px.coords)[::-1]  #no longer allowed
    p = px.reverse()

shape_feature = ShapelyFeature([p], ccrs.Geodetic(), edgecolor='black', facecolor="red")
ax.add_feature(shape_feature)
plt.show()