"I very often in my line of work get last minute calls where they ask "can you be in London tomorrow morning for a job?", and even though they might call me early in the morning LA time, there is no way for me to physically get there with the time difference lost because no airline leaves early enough. If there was a morning flight leaving LAX, I could get to London in time, but they all leave in the afternoon."
rereading this I'm a bit baffled
if someone calls you first thing LA time you might be able to get to the airport in time to get the 15:35 flight to London getting in at 09 00 - that still gives you most of a day in London
If they call you late afternoon and you were able to get a flight at say 08:00 from LAX the next morning you would get in around midnight to 02:00 into London - what's the difference - you get 6 hours sleep on the ground but it's still the next day when you start work??