TBIT would be my choice. There are armrest-free benches landside and others are sleeping over, so you're more inconspicuous. LAX cops do roust homeless people but all you need to do is show your ticket. If you can clear TSA, the T6 ↔ T7 and T7 ↔ T8 connectors are on the concourse level. You're not really bothered by announcements on those long elevated walkways - perfect for overnighting. Take a blanket, though.