Or is it possible to simplify your trip to HKG-MAD-LIM//SCL-MAD-HKG, keep it as a AM award costing 175,000AM not 190,000?
LHR is skipped (buy it as a stand-alone to/from MAD and/or redeem it with Avios? It's peanuts), and your MAD-LIM and SCL-MAD airline has to be the same.