The issue occurs when the difference between the longitudes of 2 consecutive points in the path is >=180
the longitudes of the first 2 points are -97 and 93, so that's the problem in this case(difference is 190)
The only thing I may suggest so far is to split this portion of the path:
new google.maps.LatLng(81, -97),
//additional point
new google.maps.LatLng(80.5, -12),
new google.maps.LatLng(80, 93),
new google.maps.LatLng(56, 78),
new google.maps.LatLng(60, -94)
Demo: http://jsfiddle.net/doktormolle/39CtV/
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