Thanks for the advice, all! I was wondering if BA will see two bookings that somewhat conflict and cancel one automatically, which happens on AA when conflicting flights are booked. Example: The AA partner award flies out June 1, arrives at LHR June 2, and connects to a short haul BA flight that also arrives June 2. The direct-booked BA avios flight flies out June 2, arrives June 3, and connects to a short haul BA flight that also arrives June 3.

When I was dealing with BA on the phone, they were able to see the AA-booked BA flight under my name and they asked if I was planning to cancel it myself.