If you were to start the ticket in SFO and route up during lunchtime from LAX on a separate ticket then you would have no starting LAX stopover and you would not have the point of origin issue.

The only stopover that is requested is JFK at the end of the trip, all the rest would appear to be mileage run stuff. Therefore, you could come in from Australia to LAX and take this as stop one for two days, as requested. Then to JFK as stop two (as requested), back to LAX with onward connection to SFO on another coupon and throw it away. That would ensure that you start and finish in the same place (if necessary for North America starting/finishing with no open sector but I cannot see this in the rules) . Just watch the trans-continental rule.

I do not think that the SYD to JFK sector will work as the purchaser wants to get off at LAX for a couple of days.