I have booked a miles award ticket LHR-BKK in J using my BA miles.

I only have BAEC Blue status but I do have Oneworld Sapphire status (courtesy of AA Platinum). On revenue tickets, I can book seating free of charge courtesy of the Oneworld status (either by quoting my AA flyer number on booking or by calling up to swap the BA number for my AA number, at least for long enough to assign the seat for free).

Does anyone know whether this flexibility applies to award flights or whether my BA number is now locked into the award booking and cannot be changed?