In Matrix, select multi city and then use the "Cheapest Available" cabin setting (as the fare allows booking in BA Y class on flights where I class isn't available). Specify Z class for the LA coded legs. You can book with the links in the Matrix powertools.

The search below includes a big chunk of UK taxes and 2x $100 stopover surcharges that can be removed by having less than 24 hours between flights in London - I've included it to demonstrate the flexibility of the fare (ie that stopovers don't trigger a HIP despite this ostensibly being a MPM fare)