It’s been a while since I did it, but LON-JFK-SCL (BA/AA then LAN) was my preferred route. I never had any issues with Lan’s service, and tended to break up the journey in NY for a day or two. Also worth looking at LON-BOG-SCL, which can sometimes have good prices. I had AMS-DFW-BOG-SCL and back booked for last week (business trip/tier point run) for under €3k in J, but had to drop it last minute.