You would be able to reclear security in several places between TBIT and T7, and it is very unlikely that there will be a long line in all these locations. Your options would include inside TBIT, after rechecking your bags, as well as in T4, T5, T6, and T7. T6 and T7 would be the easiest places to reenter, as you would avoid the T4-T6 tunnel, but even that is not a big deal unless you are very short on time. I have walked between TBIT and T7, both landside and airside, on numerous occasions over the years, and it is no more arduous or stressful than navigating through some of the larger terminals in Europe and Asia.

One of the best things about LAX is that the security entrances are spread out among eight interconnected terminals, and you can enter at any terminal. In practice that means that the security lines are almost never going to be terrible. If one terminal is backed up, you can just walk a few minutes over to the next terminal and enter there.