I ran your itinerary thru the OneWorld RTW validator:
1: IST-LHR: 1st of 4 (Europe)
2: LHR-BKK: intercontinental
3: BKK-HKG: 1st of 4 (Asia)
4: HKG-NRT: 2nd of 4 (Asia)
5: NRT-HKG: 3rd of 4 (Asia)
6: HKG-PER: intercontinental
7: PER-ASP: 1st of 4 (Southwest Pacific)
8: ASP-MEL: 2nd of 4 (Southwest Pacific)
9: MEL-SYD: 3rd of 4 (Southwest Pacific)
10: SYD-AKL: 4th of 4 (Southwest Pacific)
11: AKL-SCL: intercontinental
12: SCL-LIM: 1st of 4 (South America)
13: LIM-EZE: 2nd of 4 (South America)
14: EZE-GRU: 3rd of 4 (South America)
15: GRU-GIG: 4th of 4 (South America)
16: GIG-LHR: intercontinental
17: LHR-IST: 2nd of 4 (Europe)
You've got 3 more segments you could use. It's an easy add at the end to chose LHR (or LGW) - xxx-LHR. You just have to be sure to keep only 2 stopovers in Europe.