From my experience, this is exactly what to do:

Book a ticket to LHR (they will route you through ORD or DFW).

On a completely seperate reservation, book BA flights to your onward destination using aa.com (select "one world partners" when making the reservation). With my experience, booking BA flights at aa.com is a good deal cheaper than booking directly at ba.com. These same flights however tend to me MUCH more expensive when you book them as part of your origional PNR from the states (as an AA codeshare).

Give that a try -- it always works for me. One problem is that you will have to do customs and claim your luggage at heathrow. I suggest leaving at least three hours for the layover.