Just for completeness, another option here is to fly to LAS and drive onwards to Los Angeles. It's a 4-1/2 hour drive and if Los Angeles was time-critical, it is doable.
Also, while sub-optimal, consider that WN has 10 daily frequencies on the route with tickets in the $100-110 range. BA can't book you onto WN and WN does not interline with anybody, so you are on your own, but with service running from 06:40 to 23:00, it can be a good option if you can get yourself to LAS.
Having an eye on WN and LCC's is a good idea in general. The downsides may not matter when you really have to be somewhere and can only get close.