I wouldn't be too worried about the QF93-107 change at LAX. They most likely will give you express passes if you are late which most certainly will help. That and your bags will be tagged "Business" means they should come out quickly and on a separate carousel to standard Y bags. At least that is what happened to me last week - call on the PA saying bags tagged J/F will be on one carousel, the others on a separate one. I didn't count, but it was about 15 mins from me taking my seatbelt off in PE to briskly walking down to immigration, waiting behind 3 or so people in the express line, going to the carousel where my bag came out within 1 minute (there were plenty of other bags already out, some J before F), then to customs which was another couple of minutes and then finally walking out of the terminal. I couldn't believe it.
I've flown into LAX from QF93 only a few times and every time has been a dream, even without any express or priority channels. In my experience it seems reasonably quiet at that time of morning. Every person who has told me about LAX has described it to be a nightmare but I guess I have been lucky.
You are lucky that QF107 departs from TBIT. If you had to go to T4 for a QF codeshare on AA not only would the walk take a bit longer but there would be more people at security to line up behind.
Oh, hang on to your orange express pass for another time if needed