I think I'm out of luck on this but I thought I'd ask the experts (all of you

).
My current itenerary is as follows:
ZRH-LHR-SFO
SFO-DFW-SEA
SEA-DFW
DFW-LAX-HKG-NRT
NRT-HKG-AKL
AKL-SYD
SYD-BNE
BNE-SYD-SIN-LHR
LHR-ZRH
What I may need to do is insert a stopover in SIN for business and personal reasons (I may be moving there and would like to check the place out). Under the OWE rules, I know that this is backtracking as I've already come through Asia. My question is is it possible to purchase an extra segment to make the stopover valid?
TIA,
Jenn