unless I have to make the trip a quick one (and therefore fly J to make it more bearable), my preference is to book in Y and then try to upgrade with points. As a platinum FF, if I pick my flights and dates carefully, I can almost always get an upgrade on points (well, it has worked the last 4 times anyway).
That said, on the LAX route, J seats are in high demand, so it might not be so easy. My last 2 trips to LA were for business, so was in J. You might be best to see if someone flies that route regularly and can give you hints on best flights to take to improve your chances of an upgrade(for eg, QF 25 from Mel to LA via NZ might have less demand than the direct flight).
That said, on the LAX route, J seats are in high demand, so it might not be so easy. My last 2 trips to LA were for business, so was in J. You might be best to see if someone flies that route regularly and can give you hints on best flights to take to improve your chances of an upgrade(for eg, QF 25 from Mel to LA via NZ might have less demand than the direct flight).