Not sure how you got that low mileage level on both mapper & :-: calculator - the CRS shows it as 28,951 miles, which sounds about right when you include the massive backtrack that you're doing between MEL and LAX.

Did you mean MEL-SYD-LAX as first segments and not MEL-SIN-LAX? That's 24,379 on the CRS. (Don't you just hate it when fingers run ahead of the brain ?!?!?!? ).
I personally couldn't be bothered fluffing around in Europe, especially on LH with their 50% mileage earn limit. What about a gold buying splurge in DXB en-route to home? CDG-FRA/VIE/MUC/ZRH to DXB-BKK-SIN-SYD gets you up to 24,986. Or test drive the new TG Y product through BKK, unless you have a compelling reason to fly SQ Y.