3+ hour to make a connection at LAX is not a problem as long as you are comfortable with the risk of traveling on separate tickets. The risk is really with your PHX or ORD connection and I'm not sure LA forum is a good place to ask. Perhaps the AA forum can offer better advise.

For my risk tolerance, if my outbound long haul is to a once per day type destination, I would want my connecting flights to be on the same ticket so the airline knows where you are and can decide if they want to wait for you.