Due to IRROPS I was invol changed to PHL-LAX (on US) to T6 then LAX-SYD at T7. With 78min, they wouldn't check me into my PHL-LAX flight claiming MCT. Finally they let me get on my flight after finding they just forgot my emergency contact info. I made it over just fine but my bag did not. It was labeled with a bright red "rush" tag and I suspect one of the last to get on the plane. We did arrive late, but LAX-SYD left late and they had an hour to get my bag over. My overall confidence in their baggage handling is pretty low.

Now your whole TBIT-T7 situation sounds ridiculous. You're within the MCT, they should take your bag. But after seeing the complete lack of signage at LAX and trying to find the right terminal shuttle, I've lost any confidence I have in LAX as well.