Perhaps -
LAX-AKL-SYD-<Oz>-NRT-BKK-HKG-PEK-HKG-DEL-CCU-DEL-LHR-TLV-LHR-LAX
That won't actually work because it has too many segments in Asia and there's no Oneworld service from DEL-CCU. You can check the validity of a Oneworld routing
here, (plug the routing into the "Oneworld Explorer Validator" box). Though the list of routings (Oneworld flights) this tool uses isn't always fully up to date, it's useful for helping to validate a proposed routing and/or playing with it to see what works.
what about
:
LAX-AKL-SYD-<Oz>-NRT-PEK-HKG-BKK-DEL/BOM(-CCU-DEL/BOM)-AMM-TLV-LHR/MAD/BUD-USA
with a bunch of segments to spare. MileageMonkey says the routing is valid. The main thing is, the OP has a pretty circuitous routing in Asia, which can be "straightened out" to save segments. But if the routing has to be circuitous then it's all the tougher.
I think the OP will have problems finding L availability for that many people anyway, though. Especially with the trip coming up so soon.