BrewerSEA I'm getting 15 segments for your trip.
Can I suggest you try using your last segment somewhere in the US? it's going to waste for no reason!
For example:
8. New York (JFK) - xLAX - Santiago (SCL)
Try this
JFK-xSJU-xLAX-SCL
JFK-xMIA-xLAX-SCL
Try adding something inbetween.
JFK-SJU-LAX will be all booked in D business though

JFK-MIA this will be domestic F
MIA-LAX has the 777 service so you'll get 3 class F (of course not meal)
Here is a picture of how it is