So, an update:

I spotted two seats in First pop up to Las Vegas on the day after my originally booked flight to Los Angeles. So we lose a day of our trip, but lots of that day was going to spent driving from Los Angeles to Vegas anyway, so that's not much of a hardship. Extra cost was only £160 over the economy flight. Bonus.

Now to wait to see if availability comes up for my return. Nothing at the moment.