For anyone eligible, definitely download the MPC app and have it ready just in case. I landed into LAX on Thursday, seemingly 30m behind 2 massive asian flights. Going downstairs into the immigration hall, the non-US was horrendous - the worst I have ever seen - easily a 2 hour wait.
There were a couple of MPC signs upstairs, but nothing obvious once you went down the stairs into the main hall at TBIT. I kept walking past the main immigration line towards the US/GE queues and asked someone about MPC - and was directed to a separate desk which was marked for MPC, diplomats etc, and which was also clearly being used for people with express connection tickets. Desk was no. 44 or close to that - was next to the crew entry desks.
I was through in 10m max, so easily saved 2 hours.
Interestingly BA announced MPC as part of the arrival speech, but said it was only available to US/Canadian citizens . Hopefully it remains a secret .