I have done LAX-CLT a couple of times now and usually go with the USAirways service overnight. Yes, it leaves you buggered the next day but it is better than giving up a day playing connections.

At the moment United is going one way on 6 April LAX-ORD-CLT for about US$120 (inc. taxes). The times are very comparable to the AA flight times with both arriving in to CLT about 11:30pm.

I think that this is a better price than QF points.