Forget the layover, that trans-pac will have you in ruins when you get there. The last thing you will want to do is be at the school immediately after getting to your destination. You will be a zombie.

I am currently based in SAN, and am in SYD at least once a year and return via LAX..that is a flight without the added 4.5 hours getting to MSP and it nearly kills me every time. You are looking at 24-30 hours total travel time if you are lucky (I also assume ground transportation, customs, baggae and delays). I don't care how young you are, that is a long long long journey. Each time I do the SYD-LAX run I shave beforehand and arrive with a 2 day beard. When I get home, I make sure I have a clear calendar for at least a day. I don't even have the energy to open the fridge.

Do what others have suggested and get in a day before you are supposed to show up. Get a hotel and crash there. You will sleep like a log for 20 hours. You could also stop at LAX and get room there, there are plenty around LAX and many are affordable.

That connection time is unrealistic anyhow.