I'll jump in with a reply, since I've flown this route over the years: FJ usually begins boarding 45 minutes or so prior to departure. I think checkin 45 minutes before is a bit... daring.

There are several 747s departing at these hours, so Security can be slow at LAX TBIT, with queues and lots of people who are unsure what to do speaking a polyglot of langauges and being shouted at in TSA English. There is often an elite queue - it can be a bit hidden and poorly marked, and often the queue guardian will not even mention it or wave you to it. So, if you are flying Tabua class, be sure to show your BP and ask for the elite queue (if you are flying Pacific Voyager, I think you may be stuck in the non-elite queue anyway.)