FYI all I had to do was call AA and have them replace my AA number with my BA EC Gold number in the booking.

Next, I called JAL and they were able to see my OWE status and assign the seat.

Flight was lovely, with the 4 middle seats empty, a delightful crew and excellent catering (apart from the caviar which they melded into a bitter and for me, inedible, concoction involving almonds; I didn't mind because I'm not a caviar lover anyway).