My friend kudzu is absolutely correct and if you run into an agent who won't let you MoveUp to the earlier flight just look for another agent.
As you mentioned, MoveUp does have a wrinkle in the case of routing like yours with a connection. Since MoveUp gives a seat assignment - it's basically like changing flights without the big change fee - both segments have to have seats available for you to be able to MoveUp.
If, for some reason, you can't MoveUp because the second segment doesn't have a seat available you can stand by for the earlier LAX departure. Then stand by for the earlier 2nd segment when you get to CLT.
Jim