DNW, interesting post as I was hoping to use some AA miles to fly J to Rio later in the year.
Last October I did a OW F award on which the last leg was BA F. I was not overly impressed with first class on this route so I was going to save my miles and fly J. I found that availability was reasonable in F even though I only booked a week before departure. Each Monday had at least one seat in F. BTW I ended up staying 5 weeks and changed my departure date 3 times. The last time I had a choice of leaving on a Sat or Mon which IMO is fair enough with 3 days notice.