I just ticketed two of the following, in business for January 08. I post it in case it's of assistance to anyone working on one. Total miles just over 33,000, 16 segments. It took about a month of occasional phone calls:
CCP-SCL-DFW-DTW
DTW-ORD-MAD-BCN-CAI
CAI-LHR-DEL
DEL-HKG-PEK
PEK-SYD-AKL
AKL-SCL-IPC
IPC-SCL
SCL-MIA

Obviously, I started in Concepcion to allow connections and a stopover in Santiago. I added the Miami leg at the end only because it fit with my other travel plans and didn't add to the cost, since I was still under 35,000 miles.
The AKL-IPC leg is terribly inefficient, taking me through Santiago and then backtracking, but I've always wanted to go there (IPC, that is).