Very nice analysis! How do these points compare to the 'core' of the country; the point furthest away from the boundary:
rawpolygon=Polygon/@Map[Reverse,Entity["Country","UnitedStates"]["Polygon"][[1,1]],{2}];
rawpolygon=First@TakeLargestBy[rawpolygon,Area,1]; (* main land *)
r=DiscretizeGraphics[rawpolygon];
srdf=SignedRegionDistance[r];
pts=RandomPoint[r,750]; (* get some random points inside this region *)
sols=Quiet[FindMinimum[srdf[{x,y}],{x,#[[1]]},{y,#[[2]]}]]&/@pts; (* minimize the distance function starting from various points *)
sols={#1,{x,y}/.#2}&@@@sols;
min=First[TakeSmallestBy[sols,First,1]] (* get the one that is furthest away *)
Show[{r,Graphics[Point[min[[2]]]]}]
Giving:
{-9.88794, {-98.1595, 39.1123}}
One could be even more elaborate by using GeoDistance such as to correct for the elliptical shape of the earth...
