They only gave you five days to arrange a flight to L.A.? Or was this a date you requested in an earlier correspondence?
The consular officer's email said, "I have received your certificate to come to our office and swear in as a British Citizen. We are holding a ceremony on Wednesday 15th March. I would like to know if you can make it as you are in Arizona."
This gave me the impression that the consulate had only just received the certificate and wanted to give me the option of joining a ceremony already scheduled. Otherwise I would have been listed for the next ceremony, I imagine. If so, it was very thoughtful of them.
My schedule was clear. The only downside is the cost of a plane ticket on relatively short notice. It's a short flight on a competitive route, though, so I'll happily pay a few extra bucks to get this done.