The concept (and term) in question is "minimum connecting time" or MCT.

It exists to prevent people booking unlikely connections and to protect the airline from having to look after you in the probable event you miss the connection, having implied you could make it.

As you've seen, the airline won't book a connection inside this time, and indeed the computer probably prevents it. Not even if it's at your own 'risk'.

I don't believe the concept of waitlisting applies here, as the flight isn't actually full - or at least you don't say it is.

stewaran's advice is really the best you can do. Ask when you arrive at LAX if you can change and/or standby for the earlier flight.

hth