The prices you quote include the 10% discount. Taxes, fuel fines etc will be added on at the end.
To get the tool to route you on BA through LHR to MAN you will need to force it to do so by putting in the sectors separately. Likewise force a routing via SYD on the way out of OZ and choose the QF107 flight that is a one flight number flight to JFK (even though it goes via LAX). You could also fly MEL-SYD-SFO-JFK to avoid touching LAX again.
I just successfully got it to price up the following
LAX-LHR-MAN-BKK-MEL-SYD-JFK
The all in price was 9047.58 USD.