I haven't done exactly what you are proposing, but I think when you check in in Sydney you should be able to check your bags (routing) all the way to your destination. Of course, once you land in LA, you will have to claim your bags, and go through customs. At that point, if you have tags indicating your onward flights you should be able to turn them back in just past customs. If they are not tagged, then you are going to have to go upstairs and check in. Only then will you find out if they will take your bags or not.

I have done the LA thing with shorter flight connections, and I have done 11+ hour connections from Hawaii to east coast (enough to go get a hotel for the night) and they kept my bags in that condition. 12+ hour connections from Hawaii did not work - bags would only tag to LAX.

Billy