Be aware that you are only allowed 2 stopovers in the continent of origin, so one at least of LAX, DEN, ORD has to be a transit (in other words strictly less than 24hrs between scheduled arrival and scheduled departure)

To maximise AAdvantage RDMs, consider making some AA flights in Nth America at the start of the journey (you are allowed up to 16 flights total of which up to 6 can be in Nth America), and also consider flying AA transatlantic. If you sign up for the challenge (see the sticky on the AA forum) and you can get 10K elite qualifying points on AA flights, then you can quickly achieve AAdvantage Platinum status. That will give you double RDMs on some flights, allows you to check in at business class counters, and best of all IMHO allows you into business class lounges even when flying economy.

A LONEx doesn't earn any AAdvantage miles when flying RJ or CX (and perhaps others), only 25% miles on BA, and IIRC 70% on JL (full details are available on aa.com). So by using a tool such as great circle mapper or mileage monkey, you can do the arithmetic yourself.

ps Welcome to FlyerTalk