I have booked STL-DFW-LHR on separate tickets many times. If you are using AVIOS and a companion voucher you cannot combine BA flights with AA flights and that is the only way to do it.

To the original OP, I have had the same misfortune as you. Even if on separate tickets AA have a policy to protect your onward flight on BA if they failed to get you to to the connecting point. The One World liaison desk will take care of it. You may have to ask the agent to contact them as not all of them know about that policy. Even if in one paid ticket they would look after you.