This is quite a trip. Looks to be a little over 75,000 actual flight miles. Another alternative to fix the 2 NA transcon problem is to do SCL-DFW-BOS and then add on a DFW-LAX segment to the end to use your 6th NA segment and take either AA or BA LAX-LHR, depending on where you want the miles/points.

A couple of items you may want to watch for. Chile insists that their airport tax show on the actual ticket coupon. If it's not there you will probably have to pay it again in SCL and IPC. Also, CCS has a ridiculously high airport tax that they want paid at check in, in local currency. As I recall it is about 45,000 Bolivars (around US$50).