My advice is different, very different.

Nobody likes the LAX airport experience, so like everyone else I switched to routing via HKG.....and then changed back again.

The reasons why I changed back to LAX are as follows:

1. The timing of the HKG flights is horrible. If you stopover at HKG northbound you have to set your alarm for around 3 am to get up to check in, and that is really exhausting. But even if you fly straight through, the HKG-LHR flight is a long, long day flight after a night's sleep, so you still get jetlagged. Basically the HKG route to London makes jetlag a certainty whereas you can split your sleep on the LAX route so that you sleep 4 hours AKL-LAX and 4 hours LAX-LHR, both overnight, and avoid jetlag.

2. Unless you're an avid shopper or a Macau-destined gambler, HKG is a really crappy stopover. In contrast, Los Angeles doesn't just have tacky things like Hollywood and Disneyland, but also has great nearby places for a 1 night stopover (Santa Monica Beach), a 2 night stopover (Orange County's coastline or San Diego) or a 3 night stopover (Santa Barbara or Palm Springs).

3. HKG doesn't open up any online stopover options, but LAX offers Tahiti, Hawaii, Fiji, Rarotonga, Tonga and Samoa.

So while I totally agree that the TSA make LAX an annoying airport, it is still a much better option than flying through the nicer HKG airport and getting jetlagged.